Prime Minister Alexis Tsipras says he won't resign despite being pressed to impose more austerity measures in Greece.
In an interview with state TV on Tuesday, Tsipras said "I will not run away from my responsibilities."
Tsipras is facing growing dissent within his left-wing Syriza party after breaking election campaign promises to reach a deal for a third bailout.
The prime minister criticized the deal, but said it was the best Greece could get.
Tsipras said "the policies imposed on us were irrational ... But the policies offer a course out of the crisis."
President Barack Obama has welcomed the agreement between Greece and its creditors.
In a statement Tuesday, the White House said Obama considered "the agreement a positive step that could help underpin a return to growth and debt stability in Greece" but noted that "further work will be required."
The statement followed Obama's telephone calls with French President Francois Hollande, German Chancellor Angela Merkel, British Prime Minister David Cameron and Federica Mogherini, the European Union's high representative for foreign affairs and security policy.
On Monday, the U.S. Treasury Secretary Jacob Lew had said the deal was in the best interests of Greece, Europe and the global economy.
Greece's finance ministry says the draft bill needed to start talks on Greece's third bailout has been submitted to Parliament.
The bill will be discussed Wednesday and voted on later than night. It includes reforms to Greece's consumer tax.
The deal Prime Minister Alexis Tsipras agreed to after a marathon 17-hour eurozone summit on Monday has left him facing a backlash at home. Many in his radical left Syriza party have indicated they will refuse to vote for the deal because it goes back on election pledges to repeal austerity.
The bill is expected to pass with votes from opposition parties, who have said they will support it as it was the only way to ensure Greece remains in the euro currency.
Valdis Dombrovskis, the European Union's euro commissioner, says the Greek crisis has symbolized the need for closer co-operation between the countries that use the single currency.
Dombrovskis says Tuesday that there's a big need to "strengthen the economic and monetary union."
However, he notes that the lack of European market turmoil during the Greek crisis shows that progress has been made over the past five years since the region's debt crisis first exploded.
Dombrovskis says the eurozone's integration efforts since then are having a "positive" effect.
"The eurozone is considered to be more robust to withstand shocks like this."
German Finance Minister Wolfgang Schaeuble says "it will be a challenge" to get Greece a quick loan it can use to avoid defaulting on a debt due next week, on July 20.
He says, however, that a loan needs to be found this week "if a dramatic situation is to be avoided on Monday."
Schaeuble suggested Tuesday that one solution could be to get the European Union's executive branch involved, possibly using funds from the EU budget.
Schaeuble said there's "nothing to prevent any country from voluntarily providing money to Greece for bridge financing."
He also dismissed suggestions that Greece will struggle to raise 50 billion euros from its own assets, including from privatizations, as part of the rescue deal.
Pierre Gramegna, Luxembourg's finance minister, says Europe showed progress in the months of discussions on Greece — which culminated in a 17-hour special summit of the 19 eurozone leaders.
Gramegna, whose country holds the rotating presidency of the 28-country European Union, said Tuesday that the 19-country eurozone handled the Greek crisis in a more "efficient way" than it did five years ago when Greece's debt crisis first exploded.
On Monday, Greece struck a preliminary bailout deal for a third bailout that, if concluded, will see it get enough to pay its debts over the coming three years and secure its place in the euro.
Greece was first bailed out in 2010 and the eurozone has spent much of the time since then making the single currency zone more cohesive.
Italy's finance minister says that only Italy, France and Cyprus supported a compromise deal with Greece, while the rest of the eurozone nations fell in behind Germany's hard-line position.
Pier Carlo Padoan says in an interview published Tuesday in daily Il Sole 24 Ore that he was surprised by how many countries fell in behind Germany, and that "in the end, only we, the French and little Cyprus were for a compromise."
Greece on Monday agreed on a preliminary rescue deal with its fellow eurozone partners. Before it can get loans, it has to implement a string of tough economic measures.
Padoan says, "we avoided the worst. But from today a very complex path, whose outcome can't be taken for granted."
Finnish Finance Minister Alexander Stubb is hopeful a way will be found to help Greece manage upcoming debt repayments to avoid a default.
Stubb, who has been one of Greece's most outspoken critics, says there are up to six ways to get Athens this so-called bridge financing.
He concedes it's going to be difficult for eurozone members to offer cash without any conditions attached. But he adds: "never underestimate the capacity of European lawyers and economists to come up with a solution."
Stubb says it's probably "impossible to back down at this stage" and that it's possible Greece may get bilateral loans. He also says creditors could extend the dates by which Greece has to pay its debts to when the country gets the bailout loans from a new rescue package.
Timing is everything, says Irish Finance Minister Michael Noonan, and Greece got its timing all wrong during the bailout negotiations.
After the 19 eurozone leaders reached a tentative deal to keep Greece from financial collapse on Monday, Noonan says Greece could have been in a much better situation had it clinched a deal much earlier — like in February, when it faced a first bailout deadline.
He says: "It would have been much easier to settle this last February, and it would have been much easier to settle this a fortnight ago," when Greece shocked its eurozone allies by calling a referendum and seeking to reject their latest proposals.
"From an economic, financial and social point of view it was an absolute disaster, because we all know in democracies that political success and economic success go hand in hand."
The eurozone's top official says it's not easy to find a way to get Greece a short-term cash infusion that will help it meet upcoming debt repayments.
Arriving for Tuesday's meeting of the 28 finance ministers of the European Union, Jeroen Dijsselbloem said discussions will take place over the coming couple of days on how to get Greece so-called bridge financing.
Greece does not have the money to make a 4.2 billion euro ($4.7 billion) payment to the European Central Bank on July 20. Greece is also in arrears to the IMF by around 2 billion euros.
It will take about four weeks for Greece to get access to its new bailout program, which was agreed upon in a preliminary deal on Monday.
Dijsellbloem says ministers are looking at all possible instruments and funds but all have "disadvantages or impossibilities or legal objections."
British Treasury chief George Osborne came to a European Union meeting of finance minister with a clear message — don't expect Britain, which is not part of the euro, to pay for any of Greece's rescue money.
After the 19 eurozone leaders reached a tentative deal to keep Greece from financial collapse on Monday, the focus turned to how to get Greece a first, small loan so that it can meet looming debt repayments.
Osborne says Britain, one of the nine EU nations not part of the euro, will be staying out.
He said ahead of an EU finance ministers' meeting: "The idea that British taxpayers are going to be on the line for this Greek deal is a complete non-starter. The eurozone needs to foot its own bill."