Greece is facing acute international pressure, notably from US president Barack Obama, to secure a deal with creditors amid fears of a Greek debt default and exit from the euro.
With Greece facing an end-of-month deadline to secure a deal, Mr Obama and German chancellor Angela Merkel led calls for a swift resolution to Greece's protracted bailout talks.
At the end of the G7 summit in Elmau, Germany, Mr Obama said there was a "sense of urgency" to resolve the situation.
He said: "What it's going to require is Greece being serious about making some important reforms."
The Greeks, Mr Obama added, will have to "make some tough political choices that will be good for the long term".
The US president also stressed that the international community should "recognise the extraordinary challenges that Greeks face, and if both sides are showing sufficient flexibility, then I think we can get this problem resolved".
Mrs Merkel warned time is running out, and that while Greece's euro partners want the country to remain in the eurozone, Athens has to play its part by implementing reforms.
She said: "There's not a lot of time, that's the problem, that's why we have to work as intensively as possible."
A resolution is needed by June 30, when Greece's bailout programme ends and the remaining 7.2 billion euro (£5.2 billion) in rescue loans will no longer be available. Without these funds, Greece cannot repay its debts and could end up crashing out of Europe's joint currency.
Discussions were deadlocked late last week, when Greece's prime minister Alexis Tsipras rejected as "unacceptable" a proposal from the three institutions overseeing Greece's bailout - the European Central Bank, the International Monetary Fund and European Commission.
Worries of a Greek default and euro exit kept markets in check on Monday - the Stoxx 50 index of leading European shares closed down 0.8% lower and the Athens Stock Exchange ended 2.7% lower.
Greek government spokesman Gabriel Sakellaridis said negotiators were in Brussels to explore the "scope for convergence" with creditors and indicated there was room for negotiation.
Mr Sakellaridis reiterated that Greece considers its proposal - a 47-page document delivered by Mr Tsipras during a visit to Brussels last week - to be the basis for a deal.
"The Greek negotiating team that has gone to Brussels is evidently there so as to see the scope for convergence so there can be a mutually acceptable solution to both sides," Mr Sakellaridis said.
The two sides disagree on a number of issues, such as pension cuts and labour reforms. Each side has said it expects a response to its own proposals.
Holger Schmieding of Berenberg Bank said the "room for manoeuvre looks limited," noting that hardliners within Mr Tsipras' radical left party and the government's nationalist coalition partner "may oppose almost any condition which lenders must attach to the disbursement of money".
On the lenders' side, he said, "the IMF and - to a lesser extent - the ECB seem to be against any further concessions".
Jitters over Greece swelled when the government delayed a payment due last Friday to the IMF. Instead, it opted to bundle all four IMF repayments due this month into one on June 30. Allowed under IMF rules, the option has been used only once, by Zambia in the 1980s.
Mr Tsipras on Friday described the institutions' proposals as an "unpleasant surprise," saying they ignored the progress made in the previous months.
The rejection sparked the ire of European Commission President Jean-Claude Juncker, who is considered more lenient towards Greece than the IMF, ECB and the eurozone's lead bailout contributor Germany.
"We will continue to work for a solution," Commission spokesman Margaritis Schinas said in Brussels.
"There is a position of the three institutions which is a good basis for finding a solution, provided that all sides concentrate on the remaining issues to be solved."
If no deal is secured, one possibility would be for the current bailout to be extended again. Originally due to end late last year, it has already been extended twice.
Mr Sakellaridis said this was not something the government was aiming for, and reiterated that Greece wants a comprehensive solution that will also tackle the debt issue.
Athens argues its debt, currently at more than 170% of annual economic output, is unsustainable and that some form of debt relief is needed.
He also sought to douse talk of elections, saying it was not something the government was considering. Some ministers had raised the issue as an option if a deal cannot be reached.
The current stalemate comes after five months of difficult negotiations since Mr Tsipras won January elections on promises to end austerity imposed in return for two bailouts worth 240 billion euro (£175 billion).
Finance minister Yanis Varoufakis, who was in Berlin to deliver a speech, met his German counterpart Wolfgang Schaeuble for talks that the Greek minister described as "productive".