FORM 6-K

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

Report of Foreign Private Issuer

Pursuant to rule 13a-16 or 15d-16 of

The Securities Exchange Act of 1934

For the month of June, 2013

National Bank of Greece S.A.

(Translation of registrant’s name into English)

86 Eolou Street, 10232 Athens, Greece

(Address of principal executive offices)

[Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.]

Form 20-F   x   Form 40-F  o

[Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to rule 12g3-2(b) under the Securities Exchange Act of 1934.]

Yes   o   No   x

[If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-               ]

Not for release, publication or distribution in whole or in part into the Unite d States, Australia, Canada, Japan or Italy. The Offered Securities to be issued in connection with the Offering have not been and will not be registered under the U.S Securities Act of 1933, as amended and may not be offered or sold in the United States or to, or for the account or benefit of U.S persons absent registration or an applicable exemption from such registration requirements.

ADMISSION FOR TRADING OF THE NEW SHARES AND WARRANTS ARISING FROM THE SHARE CAPITAL INCREASE OF NATIONAL BANK OF GREECE — SPECIFIC FEATURES OF THE WARRANTS

NATIONAL BANK OF GREECE SA (“ the Bank ” or “ NBG ”) announces that as at 27 June 2013 its 2,274,125,874 new common, registered, voting shares (“ New Shares ”) of a nominal value of EUR 0.30 each that arose from the Bank’s share capital increase by payment in cash and contribution in kind, as per resolution of the 2nd Repeat Extraordinary General Meeting of Shareholders held on 29 April 2013 and resolution of the Bank’s Board of 20 May 2013 which set out in detail, inter alia, the resolutions of the said General Meeting (“ the Increase ”), will commence trading on the Athens Exchange (the “ ATHEX ”). As of the same date, the new aggregate of NBG shares listed on the ATHEX will be 2,396,785,994 common, registered voting shares of a nominal value of EUR 0.30 each.

As of the same date the trading of 245,779,626 Warrants will commence; the said Warrants will be issued by the HFSF and granted to private investors who participated in the Increase in accordance with Law 3864/2010 and Cabinet Acts 38/2012 and 6/2013. The start-of-day price of the Warrants will be fixed in accordance with ATHEX Board Decision 33/23.05.2013.

As at 25 June 2013, the ATHEX approved the admission for trading of the New Shares and the Warrants on the ATHEX. The New Shares and Warrants will have been credited to the beneficiaries’ Investor securities accounts in the Dematerialized Securities System (DSS) upon commencement of trading as at 27 June 2013.

Specific Information on the Warrants

Warrants constitute freely transferable securities. Each warrant incorporates its holder’s right to purchase from the Hellenic Financial Stability Fund (the “ HFSF ”) 8.22923881005499 New Shares acquired by the HFSF as a result of its participation in the Increase (the “ Purchase Right ”). The date of issue of the Warrants is 26 June 2013 (the “ Issue Date ”). Warrants do not offer voting rights to the beneficiaries or holders thereof.

Warrants may be exercised every six (6) months, the first exercise date being the six-month anniversary of the Warrant issue date and the last exercise date up to fifty-four (54) months from the date of issue of the Warrants. Purchase Rights that are not exercised by the final exercise date, as above, shall ipso jure lapse and the respective Warrants shall be cancelled by the HFSF. The procedure for exercising the Purchase Rights and the settlement thereof and any change in the rights and obligations of the Warrant holders that may occur as long as the Warrants are valid, shall be announced by the Bank via its webpage and the ATHEX Daily Price List, at least 10 days before each Warrant exercise date.

2

The strike price of the Purchase Right corresponding to each Warrant for the acquisition of New Shares held by the HFSF (the “ Strike Price ”) shall be equal to €4.29 plus accrued interest at an annual rate of 3% plus a margin of:

on the number of New Shares that Warrant holders are entitled to upon exercise of their rights. The Strike Price shall be adjusted accordingly in the event of corporate acts and announced through the Bank’s website and the ATHEX Daily Price List.

The following table sets out the prices for the acquisition of one underlying share of the Warrant, per semester, based on the Offer Price of €4.29, without taking into consideration any corporate acts:

* If the scheduled Exercise Date does not fall on a business day, the immediately following business day shall be deemed the Exercise Date and interest adjusted accordingly.

** The last Exercise Date, i.e. 26 December 2017, is the Maturity Date of the Warrants.

*** After 36 months as of the issue of the Warrants, the HFSF is entitled, subject to certain requirements, to transfer the underlying common shares to third parties free of any obligation to indemnify accordingly Warrant holders who choose not to purchase such shares.

The Warrants shall be traded in dematerialized form under the Warrants Trading Category, under ISIN GRR000000036 and OASIS ETETΠ codes in Greek and ETEW in Latin characters.

For further information, investors may contact NBG’s Shareholder Services Department at (tel. +30 210 3343415, +30 210 3343416, +30 210 3343419, +210 3343421, +30 210 3343436 & +30 210 3343412).

Athens, 25 June 2013

3

United States

This release is not an offer for sale of securities in the United States. The Offer is not being made, directly or indirectly, in or into or by the use of the mails or any means or instrumentality (including, without limitation, facsimile, telex, telephone, email and other forms of electronic transmission) of interstate or foreign commerce of, or any facilities of a national securities exchange of, the United States.  Accordingly, copies of this Release, the Offering Circular, as supplemented by the Offering Circular Supplement and any related offering documents are not being, and must not be, mailed or otherwise distributed or sent in, into or from the United States or to or from U.S. persons.  Persons receiving this Release, the Offering Circular, as supplemented by the Offering Circular Supplement and any related offering documents (including without limitation custodians, nominees and trustees) must not distribute or send them in, into or from the United States.  Doing so may invalidate any purported acceptance.

European Economic Area

This release is only addressed to persons in member states of the European Economic Area who are “qualified investors” within the meaning of Article 2(1)(e) of the Prospectus Directive (Directive 2003/71/EC and amendments thereto). No offer or invitation to acquire securities of National Bank of Greece S.A. is being made by or in connection with this release. Any such offer will be made solely by means of the Offering Circular, as supplemented by the Offering Circular Supplement once it has been approved by the Hellenic Capital Market Commission and published in accordance with Greek law in connection with the offer in Greece, or outside Greece in reliance upon any exemption set forth in any applicable law, rule or regulation.

United Kingdom

This release is directed in the United Kingdom solely at persons who (i) have professional experience in matters relating to investments and who fall within the meaning of Article 19(5) of the Financial Services and Markets Act 2000 (Financial Promotion  Order 2005) (the “Order”), (ii) are high net worth entities falling within Article 49(2) (A) to (D) of the Order or (iii) to persons to whom it may otherwise be lawful to communicate it to (all such persons together being referred to as “Relevant Persons”). This release must not be acted on or relied on by persons who are not Relevant Persons. Any investment or investment activity to which this release relates is available only to Relevant Persons and will be engaged in only with Relevant Persons.

Italy

No offer is being made, or will be made, directly or indirectly, in or into the Republic of Italy (“Italy”) as a public offer (as defined in article 1, paragraph 1, letter v) of the Legislative Decree no. 58 of February 24, 1998). The Offering Circular, as supplemented by the Offering Circular Supplement , this Release and any other documents or materials relating to the Offered Securites have not been submitted to the clearance procedures of the Commissione Nazionale per le Società e la Borsa (CONSOB) pursuant to Italian laws and regulations. Accordingly, shareholders located in Italy are notified that the Offering Circular, as supplemented by the Offering Circular Supplement is not intended to be addressed to them, they may not participate in the Offering and the Release and any other offering material relating to the Offering or the Offered Securities  may not be distributed or otherwise made available to them as part of the Offering.

4

Each intermediary must comply with the applicable laws and regulations concerning information duties vis-à-vis its clients in connection with the Offered Securities or the Offering.

5