Eurozone finance ministers on Tuesday backed new reforms proposed by Greece in exchange for a four-month financial lifeline that will keep the country afloat and in the single currency for the time being.
The news buoyed Europe's main stock markets, with London's benchmark index hitting a record high.
The International Monetary Fund, however, as well as the European Central Bank, expressed reservations about the plan, even though it represents an apparent climbdown for Greece's new radical left Prime Minister Alexis Tsipras.
The 19 eurozone ministers signed off in a telephone conference on the plan, which the new left-wing government submitted on Monday to meet a demand made by Greece's creditors at 11th-hour talks last week.
Several parliaments, including Germany's, must now approve the extension before the current bailout expires on Saturday, while key details must be hammered out in coming weeks.
"We avoided a crisis but there are many challenges ahead," EU Economic Affairs Commissioner Pierre Moscovici said.
Greece's finance ministry said it had "won a few weeks" of breathing space to put forward new alternatives to its loathed current bailout programme.
Athens stocks closed up 9.81 percent amid growing confidence about the agreement, which follows weeks of often bad-tempered meetings in Brussels and around the continent.
In London the FTSE 100 index reached its highest level on record, beating its previous peak in December 1999, ending the day up 0.54 percent to 6.949.63 points.
IMF chief Christine Lagarde meanwhile cautioned that the Greek list of proposals "is not conveying clear assurances that the government intends to undertake the reforms envisaged."
Greece has had to be bailed out twice -- in 2010 and 2012 -- to the tune of 240 billion euros, leaving the country with debt worth a massive 175 percent of annual economic output.
- 'Valid starting point' -
Tsipras, whose Syriza party won elections in January, has demanded an end to the bailout programme and the reduction of the harsh austerity measures imposed by Greece's main creditors -- the European Union, ECB and IMF.
The eurozone ministers said in a statement after their hour-long phone call on Tuesday that those three institutions believed Greece's new plan was "sufficiently comprehensive to be a valid starting point" for further negotiations.
"We therefore agreed to proceed with the national procedures with a view to reaching the final decision on the extension by up to four months," they said.
If the deal is now backed by the eurozone parliaments, all the parties will then have to sit down to the plan and hammer out a full agreement by the end of April, so Athens can meet debt payments falling due through June.
German Chancellor Angela Merkel -- the austerity champion at the head of Europe's biggest economy -- asked her conservative party at a meeting Tuesday to back the extension when the lower house votes on Friday, a lawmaker said.
But she stressed that the "task is by no means done", the MP said.
French President Francois Hollande hailed it as a "good compromise". Spanish Finance Minister Luis de Guindos -- whose government faces a major challenge from left-wing parties in a general election expected later this year -- said it was a "positive solution."
- 'Just a stopgap' -
The reform list unveiled by Athens includes steps to tighten up on tax collection and government spending, especially on the civil service and pensions, and crack down on corruption.
But it also contains measures to offset the pain caused by the tough austerity policies attached to the bailout programme. The measures included free electricity for 300,000 poor families, free access to health care, food and public transport coupons and aid for those on low pensions.
No sooner had the eurozone ministers announced the deal than reservations began to emerge.
ECB head Mario Draghi said some of the Greek reform plans "differ" from existing programmes, and that any new steps must be of "equal or better quality" in cutting Greece's debt.
Diplomats in Brussels said many had reservations about the accord but all recognised it was better to have an initial agreement to avoid the dangers a failure would have caused.
But Europe has in many ways just put off the challenge of dealing with Greece's long-term debt, analysts said.
"This deal is just a stopgap, and nothing has yet been done to tackle Greece’s unsustainable debt position," Jennifer McKeown of Capital Economics said. "A disorderly default and euro exit remains a distinct possibility in future."