The plans contain controversial elements, including pension reforms and tax rises, that were rejected at a referendum called by PM Alexis Tsipras.
The EU and other creditors are studying the plans before a summit on Sunday.
France and Italy welcomed the proposals but Germany, Greece’s biggest creditor, warned of little room for compromise.
Italian Prime Minister Matteo Renzi said he was optimistic and hoped a deal could be struck on Saturday so that the Sunday meetings would not be needed.
French President Francois Hollande said the new proposals were “serious and credible” and that the “Greeks have just shown their determination to remain in the eurozone”.
Only a few days ago Mr Tsipras won an overwhelming mandate from the Greek people, in a referendum, to reject more-or-less these bailout terms.
And today, on the back of that popular vote, he is signing up to the supposedly hated bailout. This is big politics that would make Lewis Carroll proud.
But here’s the point. If a way isn’t found to allow the banks to reopen within days – and the ECB simply maintaining Emergency Liquidity Assistance won’t come anywhere near to achieving that – the Greek economy will implode so that any bailout deal agreed this weekend will become irrelevant in weeks.
But Germany has taken a more cautious line. Eurozone finance ministers are meeting in Brussels on Saturday – German finance ministry spokesman Martin Jaeger said the outcome was “completely open”.
Mr Jaeger emphasised that Germany saw “very little leeway in terms of restructuring, [or] reprofiling [Greece’s debt]”, and would not accept any reduction in debt that caused Germany more losses.
He said Finance Minister Wolfgang Schaeuble remained “sceptical” about the debate around a softening of Greek debt terms.
A meeting of eurogroup heads of government is scheduled for Sunday afternoon, followed by a full EU summit two hours later.
Jeroen Dijsselbloem, the head of the eurogroup, said the Greek proposals were “thorough” – but warned they would have to be fully reviewed.
The eurogroup is a body for eurozone ministers to discuss monetary policy.
If approved over the weekend, the proposals must also be ratified by parliaments in several EU member states before bailout funds can be released.
Some creditors are likely to ask if the proposals ask for too much in return for too little.
Meanwhile, the plans face possible opposition in Greece for having embraced many of the austerity measures rejected at a referendum last Sunday.
Parliament is debating and then voting on the plans on Friday evening.
A reduction – or writedown – in the value of a troubled borrower’s debts. In 2011, Greece’s private lenders received a massive 50% haircut of what they were owed. At this stage the Greeks are being careful not to ask for debt haircuts.
Altering the terms of a loan in order to extend the repayment period. It may also mean dismissing part of the money owed. US Treasury Secretary Jacob Lew has said Greece’s creditors should restructure the country’s debt, but that such a move would not necessarily mean writing off a part of what Greece owes them. The IMF’s boss Christine Lagarde has also said Greece needs debt restructuring.
The forgiveness of part or all of a debt (a ‘haircut’), or the temporarysuspension of repayments on the existing debt. The IMF Chief Economist Olivier Blanchard has said any Greek deal should also include debt relief.
A spokesman for Mr Tsipras’ Syriza party said he was confident MPs would give the government the mandate to negotiate the new bailout package.
The coalition government has 162 seats in the 300-strong parliament, and also has the backing of many opposition MPs.
However, the BBC’s Mark Lowen in Athens says that no matter how it is packaged and whatever the positive spin, Mr Tsipras has made a major climb-down, with the measures he has agreed similar to what the creditors were demanding.
Mr Tsipras has asked eurozone and other creditors for 53.5 billion euros ($59.47 billion) to cover Greece’s debts until 2018.
The prime minister submitted the proposals to Greece’s creditors – the European Commission, the European Central Bank and the International Monetary Fund – by the Thursday deadline they had set.
tax rise on shipping companies.
unifying VAT rates at standard 23%, including restaurants and catering.
phasing out solidarity grant for pensioners by 2019.
€300m ($332m; £216m) defence spending cuts by 2016.
privatisation of ports and sell-off of remaining shares in telecoms giant OTE.
scrapping 30% tax break for wealthiest islands.
Greece’s creditors have already provided more than €200bn in two bailouts since a rescue plan began five years ago. The second bailout expired on 30 June.
Greece’s banks are still closed and the €60 (£43; $66) daily limit on cash machine withdrawals for Greeks, imposed on 28 June, remains in force. With a shortage of €20 notes, for many the limit is in effect €50.
10 July: Greek parliament vote. ECB, EU and IMF discuss proposals at technical level.
11 July: Eurozone finance ministers discuss plans (Brussels 13:00 GMT).
12 July: Eurogroup leaders meet (14:00 GMT) followed by summit of all 28 members of the European Union (16:00 GMT). Both Brussels.
20 July: €3bn payment due from Greece to the European Central Bank.