ATHENS--Two of Greece's biggest lenders, Eurobank Ergasias and Alpha Bank, have formally requested access to an emergency cash facility run by the country's central bank, amid concerns that liquidity conditions in Greece's banking sector were tightening in the run-up to national elections later this month.

Banking officials from the two lenders said Friday that the moves were only a precaution and that neither faced an immediate cash crunch. "We have made an application to the central bank," a senior executive at one of the banks said, "but it is strictly on a precautionary basis."

A Bank of Greece official also confirmed the requests, saying that a decision will likely be taken by next week. People familiar with the matter have said that Greece's two other systemic lenders-- National Bank of Greece and Piraeus Bank--may follow suit in the coming days.

People familiar with the matter said the two lenders were seeking a few billion euros between them. Although the amount being sought is small, the move has again evoked fears over the stability of Greece's banking system as the country lurches through another period of political uncertainty ahead of polls scheduled for Jan. 25. The last time the banks started tapping the central bank's Emergency Liquidity Assistance fund was in August 2011 during the depths of Greece's protracted debt crisis.

In midday trade Friday, Greek bond prices sank, with the price on the benchmark 10-year government bond jumping roughly 0.4 percentage point to 9.5%. Greek equities tumbled, pushing the general index 3.2% lower to below the psychologically important 800-point level. Greek banks stocks were between 6% and 8.5% down.

Since the start of the crisis in late 2009, Greek banks have been hit hard. Over the past five years, skittish depositors have withdrawn some EUR70 billion ($81 billion) from Greece's banking system; nonperforming loans now account for more than a third of banking system loans; and the banks have had to write down billions in euros in losses from an unprecedented EUR200 billion sovereign-debt restructuring in early 2012.

Largely cut off from interbank lending, the Greek banks were also forced to resort to the European Central Bank--and later the Bank of Greece--for their cash needs. In May of 2012, as Greece faced the first of two elections that year, Greek bank borrowings from the ELA peaked at EUR124 billion. Since then, the banks have paid back all their relatively pricey ELA loans, but according to the latest data from November, were still borrowing EUR44.9 billion from the ECB.

But as Greece heads to the polls a week from Sunday, Greek banks are again being squeezed. In the past two months, some EUR3 billion of deposits have again fled the banking system and there are signs that other banks in Europe are reining in their interbank lending to Greek banks. Also worrying is an impending deadline for Greece to hammer out a new aid package to replace its existing EUR240 billion bailout from fellow eurozone countries and the International Monetary Fund.

The current package runs out at the end of February--a month after the elections--and without a new deal, Greek banks won't be able to borrow fresh funds from the ECB. Instead, they will have to rely on the ELA for their cash needs.

That would come at a cost though: the Bank of Greece charges a 1.55% interest rate for its cash, compared with 0.05% for the ECB. Greek government officials estimate that a switch from one to the other could cost the banks more than EUR1 billion in foregone profits this year, something that would further crimp their ability to take provisions for bad loans or finance Greek households and businesses.

"We did make an application for ELA lending to the Bank of Greece," said a senior official at one of the two lenders. "On March 1, the current program comes to an end and, just in case, it is a sensible move, it's just to be on the safe side. The amount we are seeking is small, well below 5 billion euros, but in a worst-case scenario, you may need it."

Nektaria Stamouli in Athens, and Simon Clark and Anuj Gangahar in London contributed to this article.

Write to Alkman Granitsas at alkman.granitsas@wsj.com

Access Investor Kit for National Bank of Greece SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=GRS003003019

Access Investor Kit for Bank of Greece SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=GRS004013009

Access Investor Kit for Piraeus Bank SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=GRS014003008

Access Investor Kit for Alpha Bank SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=GRS015013006

Access Investor Kit for Eurobank Ergasias SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=GRS323003004

Access Investor Kit for Alpha Bank SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=US02071M1018

Access Investor Kit for Eurobank Ergasias SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=US26844B2097

Access Investor Kit for National Bank of Greece SA

Visit http://www.companyspotlight.com/partner?cp_code=P479&isin=US6336437057

Subscribe to WSJ: http://online.wsj.com?mod=djnwires