Talks between Greece and its eurozone creditors broke down early Thursday without even a plan of action on how to move forward on the country's debts and bailout, but markets were buoyant on hopes that a deal will be reached in time for Greece to avoid a potential exit from the euro.

Following an emergency meeting of the eurozone's 19 finance ministers in Brussels, the two sides failed to even issue a statement, a sign they will need to yield some ground if a compromise deal is to be reached at a follow-up meeting on Monday.

Alexis Tsipras, Greece's new prime minister, attending his first summit of European Union leaders, conceded that a solution will have to be based on an element of give-and-take by both sides.

"We will need to find a solution that respects the positions of all parties, so this agreement will have to be based on the core values of Europe, democracy and the vote of the people, but also on the necessity to respect the European rules," he said.

Europe has been embroiled in another Greek crisis following the election of the radical-left Syriza government last month. The new government was elected on a mandate to drastically reduce the burden of the country's bailout and the associated budget austerity measures, which Tsipras blames in large part for the country's economic woes.

Despite a recent modest return to growth, the Greek economy is around 25 percent smaller than it was before the crisis and poverty and unemployment have swelled. Greece is also lumbered by its debt burden, which stands at around 175 percent of GDP, and it has repayments this year that will have trouble meeting without outside help.

With a contingent of the eurozone countries, led by Germany, insisting that discussions can only proceed if the current bailout program is extended, a standoff has taken root. Tsipras wants the current bailout, which runs out at the end of the month, to be scrapped altogether and replaced by a new one.

Despite the apparent impasse, analysts think Greece could still agree to a bailout extension provided the required budget austerity measures are eased and Greece implements further reforms. Tsipras said his government was willing to launch further structural reforms "against tax evasion, fighting against corruption, fighting against a state based on clientelism."

Most investors think the outlines of a deal are emerging but nothing's certain.

"It comes down to: if you change the terms and conditions of a contract, have you created a new contract or do you have the same contract with minor amendments?" said Gary Jenkins, chief credit strategist at LNG Capital. Though Jenkins thinks a deal is "doable," he cautioned that this could develop into a "case where pride really could come before a fall."

Most stock markets were higher Thursday, likely buoyed also by the cease-fire announced in Ukraine. Athens' main index was over 3 percent higher, suggesting Greek investors have taken the lack of progress in the talks in stride.

Greece's finance minister, Yanis Varoufakis, said a deal at the meeting, his first since taking office, was never on the cards, but he laid out hope that progress was possible Monday.

"We understand each other much, much better now than we did this morning, so I think this is a major achievement because, you know, from understanding, the agreement follows," he said.

He stressed that Greece would insist on agreeing on a new bailout program, rather than extending the current one, which "has been catastrophic."

Jeroen Dijsselbloem, the head of the eurogroup of finance ministers, said detailed proposals weren't even discussed at the meeting, adding that there wasn't enough common ground to chart the road to the next meeting.

"It was my ambition to agree on the steps to take the next couple of days so we could spend them well and make more progress between now and Monday," he said. "Unfortunately we've not been able to do that so we will continue our talks on Monday and move on from there."

Popular support for a change of course is strong in Greece, with thousands taking to the streets across the country Wednesday.

Since winning the Greek general election last month, the Greek government has outlined its broad ambitions but it has still to present concrete proposals. Varoufakis has said he wants to scrap Greece's current bailout program and agree on a new one. Without the bailout's financial support, Greece faces bankruptcy — and a possible exit from the eurozone, a development that could further damage Greece's economy at least in the short-term, and throw global financial markets into turmoil.

Varoufakis has suggested Greece be granted a "bridging loan" to tide it over for a few months. In return, Greece would commit to further reforms, particularly on how to deal with the country's notoriously inefficient tax system.