The talks are aimed at striking a deal on the request made on Thursday by Greece for a new six-month bailout.
Germany rejected the request despite it being welcomed by the European Commission.
The existing bailout deal expires at the end of the month and Greece could run out of money without a new accord.
Germany’s Wolfgang Schaeuble and Greece’s Yanis Varoufakis are meeting in Brussels with IMF managing director Christine Lagarde and Jeroen Dijsselbloem, the Dutch finance minister who heads the Eurogroup.
During a break in the talks, Mr Dijsselbloem said the situation was quite complicated: “I am talking to the main players trying to find a solution. It will take some time, but there is still reason for some optimism, but it is still very difficult. I hope to tell you the outcome in a couple of hours time.”
The unscheduled negotiations have delayed the start of the finance ministers’ meeting, which was due to commence at 1400 GMT.
Arriving for the Eurogroup meeting, Mr Varoufakis said he hoped there would be a deal struck on Friday.
“The Greek government has not just gone the extra mile, but the extra 10 miles, and now we are expecting our partners not to meet us halfway, but a fifth of the way… Hopefully at the end of this, we come out with some white smoke,” he said.
Meanwhile, French President Francois Hollande reiterated that Greece belonged in the eurozone and there were no plans for it leaving, following talks in Paris with German Chancellor Angela Merkel.
“Greece is in the eurozone and it must remain in the eurozone,” he told a joint news conference with Mrs Merkel.
Mrs Merkel said German politicians were “very much geared towards Greece remaining in the euro”, adding that the Greek people had “made a lot of sacrifices” to do so.
However, she said there was a need for “significant improvements in the substance” of the Greek request ahead of a vote in the German parliament next week.
Earlier on Friday the German government’s stance appeared to soften after a spokeswoman for Mrs Merkel said Greece’s request for a loan extension from its eurozone partners provided “a starting point” for more talks.
“From the German government’s point of view, [the request] is still not sufficient,” said Christiane Wirtz. But “it certainly offers a starting point for further talks.”
One Greek government official described the phone call as “constructive”, adding: “The conversation was held in a positive climate, geared towards finding a mutually beneficial solution for Greece and the eurozone.”
Germany stands to lose up to €80bn if Greece were to leave the eurozone.
Greece has certainly shifted its position. The letter from the Finance Minister, Yanis Varoufakis, to the Eurogroup asked for a six-month master financial assistance facility agreement.
Payments under that agreement require Greece to comply with the measures set out in another document, the memorandum of understanding.
That is the hated economic policy programme agreed with the equally hated bailout lenders.
In the meantime, Mr Varoufakis was offering to refrain from unilateral actions that that would undermine the fiscal targets, economic recovery and financial stability and to ensure any new measures were fully funded.
Those certainly look like concessions to Germany and others.
What Berlin doesn’t like is the manifest desire of the Greek government to use the proposed extension to revise the programme.
Mr Tsipras won elections in late January on a platform of rejecting the austerity measures tied to the bailout.
A Greek government source said on Thursday the Eurogroup had “just two choices: to accept or reject the Greek request. We will now discover who wants to find a solution, and who does not”.
Greece formally requested a six-month extension to its eurozone loan agreement on Thursday, offering major concessions as it raced to avoid running out of cash within weeks.