ATHENS, Greece — Rival Greek party leaders were locked in a second day of power-sharing talks on Tuesday, with two potential minority partners voicing hope that a pro-bailout coalition government can be quickly formed after the debt-crippled country’s second inconclusive election in six weeks.

At the core of any administration will be Antonis Samaras’ New Democracy party, which came first in Sunday’s vote and won 129 of Parliament’s 300 seats — but not enough to govern alone.

Samaras is seeking an alliance with the third-placed Socialist PASOK and the smaller Democratic Left party, which would broadly fulfill Greece’s pledges to its bailout creditors for further cutbacks and reforms, keeping the country within Europe’s joint currency. Otherwise, Greece would run out of cash and the continent could plunge deeper into a financial nightmare with global repercussions.

The main sticking point promises to be how much Greece is willing to tempt fate by seeking a more lenient deal from creditors fed up with missed targets and broken reform pledges.

PASOK leader Evangelos Venizelos met Tuesday with Democratic Left head Fotis Kouvelis, who told reporters afterward that a three-party deal could potentially be achieved “within hours.”

Kouvelis said parties first had to agree on a policy platform, and on who would be appointed to the cabinet.

“I believe the process is gathering speed, the country must have a government ... and in the next hours, if there is an agreement ... it will be possible for us to proceed,” he said. Kouvelis insisted that parts of Greece’s harsh austerity program must be revised, saying the country “has been pulverized by pitiless measures.”

Venizelos, who has pressed for an agreement by Tuesday night, said he was optimistic a deal could be reached.

“I am confident after my meeting with Mr Kouvelis, our views are very close,” he said. “Greece must — and will — have a government as soon as possible. We agreed that the necessary processes must be accelerated.”

Both the conservatives and PASOK have pledged to respect the commitments for further austerity and reforms that Greece undertook as conditions for two massive international bailouts since May 2010. They are pressing for an extension of at least two years in the deadline, which would alleviate the immediate impact of new cutbacks and is seen as a likely concession by creditors. The Democratic Left is anti-austerity in principle, but wavering.

Austrian Finance Minister Maria Fekter said any changes to the bailout deal would be “an adaptation of a pragmatic nature” after debt inspectors from major creditors visit Athens.

A European Union official said the terms of Greece’s bailout will be renegotiated because worsening economic conditions have made the old agreement an “illusion.”

He said that the goals of the agreement would still be to reduce Greece’s debt and reform its economy to make it competitive. But how they are achieved would be up for discussion, the official said on condition of anonymity, citing policy.

The second-placed, anti-bailout Syriza radical left party has refused to join in a coalition. Party leader Alexis Tsipras campaigned on a strong anti-bailout ticket, vowing to scrap the country’s pledges and play tough with creditors — Greece’s European partners and the International Monetary Fund. His message resonated strongly with an austerity-weary electorate, which propelled Syriza from 4.6 percent in 2009 to nearly 27 percent and gave anti-austerity parties more than 50 percent in total.

The reasons are visible around the country. As more than four years of recession and dwindling incomes take their toll, tens of thousands of businesses have closed, unemployment is above 22 percent and many Greeks see emigration as their only hope for a decent life.

In order to pass most laws, a government needs a simple majority of 151 seats. But to have any chance of success, it would require considerably more than that, especially amid the social turmoil of the past two-and-a-half years of harsh austerity in Greece.

Together with PASOK and the Democratic Left, Samaras’ party would have 179 legislators, enjoying a strong majority of 28 seats.

Hopes that a deal can be struck boosted Greek share prices, with the battered Athens stock exchange gaining 2.9 percent in afternoon trading.

Greece’s short-term borrowing costs declined slightly on Tuesday, with the interest for a new 13-week treasury bill issue reaching 4.31 percent, down from 4.34 percent last month.

The total sum raised was (euro) 1.3 billion ($1.64 billion), with the auction 2.2 times oversubscribed.

Samaras’ three-day mandate to form a government expires on Wednesday. If it fails, Syriza would get a chance to form a government, followed by the Socialists. But Tsipras has said he will not even try to create a government. Venizelos has advocated circumventing the mandate process and proceeding straight to a meeting of party leaders under President Karolos Papoulias.

Venizelos has insisted that Syriza should participate in any coalition government, in what appears more an attempt to show the left-wing party up as intransigent rather than a realistic effort to drag it into governance.

Setting apart their bitter rivalry stemming from four decades of what was effectively a two-party system, New Democracy and PASOK took part in a brief coalition government earlier this year.