Eurozone finance ministers have approved reform proposals submitted by Greece as a condition for extending its bailout by four months, officials say.
The Eurogroup said it had agreed to begin national procedures - parliamentary votes in several states to give the deal final approval.
The measures offered by Greece include combating tax evasion and reforming the public sector.
But the head of the IMF said they lacked "clear assurances" in key areas.
Greece's debt stands at more than €320bn (£237bn), and its current €240bn bailout expires on Saturday. Fresh funding will not be released until Greece's proposals are approved in detail.
The stakes of talks over continued financial aid have been high because of fears of a Greek default that could push it out of the euro, triggering turmoil in the EU.
The main stock market in Athens rose by nearly 10% on Tuesday afternoon, hitting a three-month high.
The Eurogroup said in a statement: "We call on the Greek authorities to further develop and broaden the list of reform measures, based on the current arrangement, in close co-ordination with the institutions."
The European Commission and the European Central Bank (ECB) both stated that the Greek proposals were a "valid starting point".
The agreement had "averted an immediate crisis," said European Commissioner for Economic Affairs Pierre Moscovici.
"It does not mean we approve those reforms, it means the approach is serious enough for further discussion," he added.