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 JAPAN, AUSTRALIA OR THE REPUBLIC OF ITALY

National Bank of Greece S.A.

Athens, June 17, 2013

NATIONAL BANK OF GREECE S.A. OUTSTANDING CASH TENDER OFFER FOR UP TO 22,500,000 OF THE OUTSTANDING 25,000,000 AMERICAN DEPOSITARY SHARES, EACH REPRESENTING ONE PREFERENCE SHARE OF THE BANK

On May 31, 2013, National Bank of Greece (the “Bank”) announced the launch of an offer to purchase for cash up to 22,500,000 of the outstanding 25,000,000 American Depositary Share (ADS CUSIP 633643507) (each, and “ADS” and collectively the “ADSs”), each representing one of its Non-Cumulative Preference Shares Series A, nominal value €0.30 per share (the “Preference Shares”) upon the terms and subject to the conditions set forth in the Offer to Purchase dated May 31, 2013 (the “Offer to Purchase”) and the accompanying Letter of Transmittal, which, each as may be amended or supplemented from time to time, constitute the offer (the “Offer”).

In response to queries from investors the Bank would like to clarify that, as stated in the Offer to Purchase and the accompanying Letter of Transmittal, the Offer relates solely to the Bank’s ADSs representing its Preference Shares and not the Bank’s American Depositary Shares representing its ordinary shares.

FURTHER INFORMATION

In connection with the Offer, Bank of America Merrill Lynch is acting as Dealer Manager, D.F. King Worldwide is acting as Information Agent and The Bank of New York Mellon is acting as the Tender Agent.

The Bank has agreed to pay to each Retail Processing Dealer a Retail Processing Fee related to the tender of the ADSs under certain circumstances, as described further in the Offer to Purchase.

The Bank filed on May 31, 2013 a Tender Offer Statement on Schedule TO (a “Tender Offer Statement”), together with the Offer to Purchase and related Letter of Transmittal that are exhibits to the Tender Offer Statement, with the Securities and Exchange Commission (the “SEC”), has filed amendments thereto, and may file further amendments. Each such document, as well as any amendments, supplements or additional exhibits thereto, will be available when filed by the Bank, free of charge, from the SEC’s website at http://www.sec.gov. Holders of ADSs are encouraged to read these documents, as they contain important information about the Offer.

Requests for documents and information should be directed to the Dealer Manager and the Information Agent for this Offer.

DISCLAIMER

This press release must be read in conjunction with the Offer to Purchase and accompanying Letter of Transmittal, each as may be amended supplemented from time to time. The Offer to Purchase and accompanying Letter of Transmittal contain important information which must be read carefully before any

decision is made with respect to the Offer described in this press release. If any holder of ADSs is in any doubt as to the action it should take, it is recommended to seek its own legal, tax and financial advice, including as to any tax consequences, from its stockbroker, bank manager, counsel, accountant or other independent financial adviser. Any holder of ADSs whose ADSs are held on its behalf by a broker, dealer, bank, custodian, trust company or other nominee must contact such entity if it wishes to participate in the Offer. None of the Bank, the Dealer Manager, the Tender Agent, the Information Agent or any of their respective affiliates, makes any recommendation as to whether or not any holder of ADSs should tender ADSs held by them pursuant to the Offer.

OFFER AND DISTRIBUTION RESTRICTIONS

General

This press release does not constitute an offer to buy or the solicitation of an offer to sell Preference Shares or ADSs, and tenders of ADSs in the Offer will not be accepted from ADS Holders, in any circumstances in which such offer or solicitation is unlawful. In those jurisdictions where the securities, “blue sky” or other laws require an Offer to be made by a licensed broker or dealer and the Dealer Manager or any of its affiliates is such a licensed broker or dealer in such jurisdictions, such Offer shall be deemed to be made by the Dealer Manager or affiliate (as the case may be) on behalf of the Bank in such jurisdictions.

Hellenic Republic

Neither the press release nor any other documents or materials relating to the Offer constitute a “public offer” ( dimossia prosfora ), within the meaning of Greek Law 3401/2005, or a “tender offer” ( dimossia protassi ), within the meaning of Greek Law 3461/2006, for the purchase, sale or exchange of securities in the Hellenic Republic and no information contained herein or therein can be considered as investment advice or a solicitation of an investment in securities in the Hellenic Republic in terms of Greek Law 3606/2007. Accordingly, neither this press release nor any other documents or materials relating to the Offer have or will be submitted to the Hellenic Capital Market Commission for approval pursuant to such laws.

Republic of Italy

The Offer is not being made, directly or indirectly, in the Republic of Italy. The Offer and this press release and any other documents or materials relating to the Offer have not been submitted to the clearance procedure of the Commissione Nazionale per le Società e la Borsa pursuant to Italian laws and regulations. Accordingly, (i) neither this press release, nor any other offering material relating to the Offer or the ADSs may be distributed or made available in the Republic of Italy and (ii) no marketing, promotional, informative or solicitation activity may be performed in the Republic of Italy.

Each intermediary must comply with the applicable laws and regulations concerning information duties vis-à-vis its clients in connection with the ADSs or this Offer.

United Kingdom

The communication of this press release and any other documents or materials relating to the Offer is not being made and such documents and/or materials have not been approved by an authorized person for the purposes of section 21 of the Financial Services and Markets Act 2000. Accordingly, such documents and/or materials are not being distributed to, and must not be passed on to, the general public in the United Kingdom. The communication of such documents and/or materials as a financial promotion is only being made to those persons in the United Kingdom falling within the definition of investment professionals (as defined in Article 19(5) of the Financial Promotion Order) or any other persons to whom it may otherwise lawfully be made under the Financial Promotion Order.

2

Kingdom of Belgium

Neither this press release nor any other documents or materials relating to the Offer have been submitted to or will be submitted for approval or recognition to the Belgian Financial Services and Markets Authority ( Autorité des services et marchés financiers/Autoriteit voor Financiële Diensten en Markten ) and, accordingly, the Offer may not be made in the Kingdom of Belgium (“Belgium”) by way of a public offering, as defined in Article 3 of the Belgian Law of 1 April 2007 on public takeover bids (as amended or replaced from time to time) (the “Law of 1 April 2007”). Accordingly, the Offer may not be advertised, and neither this press release nor any other documents or materials relating to the Offer has been or shall be distributed or made available, directly or indirectly, to any person in Belgium to the extent that this would constitute a public offering in Belgium.

Republic of France

Neither this press release nor any other documents or materials relating to the Offer has been nor will be submitted for clearance to nor approved by the Autorité des Marchés Financiers pursuant to French laws and reguatlions. Accordingly, (i) neither this press release nor any other marketing paterials relating oth e Offer or the ADSs mya be distributed or made available in the Republic of France (“France”); and (ii) no marketing, promotional, informative or solicitation activity may be performed in France. Each broker or securities intermediary must comply with applicable laws and regulations concerning information duties vis-à-vis its clients in connection with the ADSs or this press release.

Grand Duchy of Luxembourg

Under no circumstances shall this press release constitute an offer to sell or issue ADSs, or the solicitation of an offer to buy or subscribe for ADSs, addressed to the public in the Grand Duchy of Luxembourg.

3