Athens, Greece (CNN) -- The planned reshuffling of Greece's Cabinet has been delayed, and the new Cabinet members will be sworn in at 1 p.m. Friday, state television reported late Thursday.
The change was announced after Prime Minister George Papandreou urged his parliamentary deputies Thursday to continue working toward rebuilding Greece under a new government, yet to be announced.
"We must not flee the battle, however difficult," Papandreou said. "I have faith in our MPs, in our movement, in our historical political party. You can rely on me, and I will rely on you. We will get Greece out of this crisis."
Earlier Thursday, two members of parliament from Papandreou's ruling socialists resigned, shaking confidence in his efforts to reconstitute his Cabinet.
The prime minister has come under fire for his inability to form a coalition with conservative opposition leader Antonis Samaras, who repeated Thursday a call for elections to be held as soon as possible.
Papandreou's planned Cabinet reshuffle represents an attempt to win support for additional austerity measures intended to help the economy weather the current crisis.
Lawmakers from the prime minister's own Panhellenic Socialist Movement, also known by the Greek acronym PASOK, met in an emergency session Thursday.
Papandreou faces opposition from his party over the austerity measures, which are intended to reduce the government deficit in order to secure a second bailout package from institutions including the International Monetary Fund and the European Union.
There are fears that efforts to restructure Greece's debt could wreak havoc with Europe's banking sector, sparking investor panic like that caused by the 2008 collapse of the Lehman Brothers investment bank.
The crisis raises concerns for Europe's currency, the euro. If a struggling nation such as Greece, Portugal or Ireland were to default on its debts, it could affect the world economy.
The IMF issued a statement Thursday saying it would continue to back Greece, provided it carried out economic policy reforms agreed upon by the government.
In Washington, White House spokesman Jay Carney said U.S. officials are monitoring the situation in Greece closely but believe their European counterparts have the capacity to deal with it.
"We consider it a headwind, if you will, in terms of the global economy and therefore the domestic economy," he said.
"So far, Greece has made significant progress in terms of reforms. But it is important that the Greek government carry on with the fiscal measures and reforms that are frequently under discussion with the EU and the IMF."
The political crisis in Greece has helped send the euro down 2 points against the dollar over two days, while the credit default market now sees a 78% chance of Greece failing to pay its debts.
Many political observers were skeptical that Papandreou retains sufficient political authority to form a new government.
Vasso Papandreou, a founding member of the governing Panhellenic Socialist Movement (but of no relation to the prime minister), said this was "a critical time for the country" as she circulated a petition among party members calling for "an immediate meeting of PASOK's parliamentary group."
Asked what would be discussed at the meeting, the lawmaker replied: "Everything."
One of the two lawmakers from the party who resigned Thursday, former government Minister George Floridis, said that both Papandreou and the leader of the main conservative opposition had displayed unforgivable lack of leadership in failing to form a national coalition.
"One-party governments, even if they include broadly popular figures, cannot bring about today's difficult mission," Floridis said in an open letter.
"This is not the time for bemoaning our fate and complaining," Papandreou responded in his speech. "The next government will be more effective and proceed to make the great changes that the people want and demand."
Papandreou spoke with conservative leader Samaras by phone on Wednesday afternoon after street riots marked the introduction of a 28 billion euro ($39 billion) austerity bill in Parliament. But by evening, their talks had broken down into mutual recriminations.
The main opposition party, New Democracy, has repeatedly demanded that Papandreou quit and that a cross-party coalition renegotiate the terms of the bailout package.
Papandreou said Wednesday that he would be willing to resign if he were the only thing standing in the way of a national unity government.
The government's popularity has plunged recently, and anti-government protests turned violent Wednesday, as demonstrators threw gasoline bombs at the Ministry of Finance and police fired tear gas at protesters, police said.
On June 9, the Cabinet approved a tough five-year plan for 2011-15 and introduced a bill in Parliament to put the measures into effect.
The government has said that the passage of these additional measures is essential to Greece's securing the fifth portion of a 110 billion euro ($158 billion) bailout package that Greece signed with the European Union and the International Monetary Fund to prevent the country from defaulting on its debts.
"We stand ready to continue our support for Greece subject to adoption of the economic policy reforms agreed with the Greek authorities," said Caroline Atkinson, director of external relations at the IMF, in a statement Thursday.
Finance Minister George Papaconstantinou has said the country hopes to secure a second bailout deal this month.
The search for a second bailout comes after it became evident that Greece is unlikely to raise capital from private markets in 2012 because of the high interest rates it would face.
Papaconstantinou has also indicated that European Union members may support calls to involve the private sector.
Despite the harsh austerity measures that the Greek government has imposed, it is failing to close its budget deficit as quickly as many had hoped. The country is in recession amid its fiscal restructuring program.
The finance minister has defended the austerity plan as necessary to keep Greece solvent. The new measures will include additional taxes and an additional 20% cut in public-sector jobs.
Protesters have been gathering outside Parliament for more than three weeks as part of peaceful demonstrations against austerity measures, with some camping in the square facing Parliament.
The credit rating agency Standard & Poor's on Monday cut Greece's rating to just two notches above default, among the lowest in the world. The agency has said that a default on some debt appears "increasingly likely."
Unemployment in Greece skyrocketed to more than 16% in May, a 40% rise since last year. The European Commission has said Greece's economy was expected to shrink by 3.5% this year.
Journalists John Psaropoulos and Elinda Labropoulou contributed to this report