Greece's conservatives are hours away from forming a coalition government after their narrow election victory, it emerged Tuesday, after their leader promised to soften the punishing austerity program despite German opposition.

A relief rally on financial markets after Sunday's vote quickly fizzled as it became clear that the New Democracy party of Antonis Samaras had failed to win a strong mandate to impose the huge spending cuts and tax increases demanded by the European Union and the IMF under a bailout deal, Reuters reported.

Radical left-wing bloc Syriza and smaller parties opposed to the conditions attached to the 130 billion euro ($164 billion) bailout won around half the vote, though they took fewer seats in parliament because the electoral system rewards the first-place party wth 50 bonus seats.

Samaras met with President Karolos Papoulias and received a mandate to form a coalition, and a New Democracy source said the party expected to seal a deal Tuesday after Samaras met with the third-place Pasok Socialists and the small Democratic Left group.

Samaras said Greece would meet its commitments under the bailout, which aims to save the country from bankruptcy and an exit from the euro zone. But he added:

We will simultaneously have to make some necessary amendments to the bailout agreement, in order to relieve the people of crippling unemployment and huge hardships.

A senior New Democracy official expected agreement soon on a new Cabinet. We are going to clinch a deal tomorrow, we will form a government, said the official, who declined to be named.

It would aim to accelerate and broaden a privatization push to refill state coffers, but also ask its creditors to spread 11.7 billion euros of further austerity cuts over four years instead of two.

Pasok would also hold Cabinet posts, meaning the two parties which have dominated Greece for decades and led it into crisis would stay in power despite Syriza's strong showing. The official also expressed hope that the Democratic Left, a small, moderate leftist party, would also take part.

Pasok leader Evangelos Venizelos called for a four-party coalition government and urged it be settled by the end of Tuesday, The Wall Street Journal reported.

But later in the day, hopes that the government may be in place by nightfall appeared to fade after Fotis Kouvelis, whose Democratic Left opposed the bailout deal in the election campaign, said several points still needed to be negotiated and agreement might take longer.

There will be a government, but I don't know if it will be formed by tonight. I believe we will have reached an agreement by the end of the week, he told reporters.

Speaking to reporters after meeting with Samaras, Venizelos described Syriza's refusal to back a coalition as absolutely disappointing.

The most crucial thing for us at this monemnt is to achieve the largest possible participation in the coalition and this must happen by tomorrow night at the latest, he said. We must send abroad and to the Greek people a message of unity, social cohesion, security and one of prospect.

Samaras also met with Syriza leader Alexis Tsipras, who says he will lead the opposition, and rightist Independent Greeks party leader Panos Kammenos. Kammenos also refused to join a coalition but said he will support some reforms to be pushed through by the cross-party government.

We will assume the responsibility of the opposition, and we plan to keep the government in check, said Tsipras, the young, brash leader of Syriza, which grabbed 27 percent of the vote Sunday, more than double the 12 percent it won in inconclusive polls last month, the Los Angeles Times reported. 

There were mixed signals from Europe over the extent of any possible changes to the bailout deal. Euro zone paymaster Germany, already irritated at what it sees as the slow pace of Greek reform, ruled out more than minor delays to some targets in the rescue package - Greece's second since 2010.

Chancellor Angela Merkel said at a meeting of G20 leaders in Mexico that any loosening of Greece's agreed reform promises would be unacceptable. The new government will and must stick to the commitments, which the country has agreed on, she said.

A New Democracy source told Reuters that Pasok would join the government, rather than just vote with it in parliament. They will participate actively, more than symbolically, and for a long time, said the official.

Kouvelis of the Democratic Left said he was ready to support Samaras, depending on the content of what is agreed. Kouvelis has also called for the bailout terms to be eased.

New Democracy won 29.7 percent of the vote, ahead of Syriza at 27 percent and Pasok at 12.3 percent. With New Democracy's 50-seat bonus for coming first, a New Democracy-Pasok alliance would have 162 seats in the 300-seat parliament. Adding the Democratic Left would give it 179 seats.