Capital controls in Greece need to be lifted immediately, Prime Minister Alexis Tsipras has told the European Central Bank.
During a phone call with Mario Draghi, the bank's president, Mr Tsipras also discussed the liquidity of Greek banks, a government official told Reuters.
The Greek government imposed capital controls to prevent the collapse of the banking system, resulting in banks closing and a limit on the level of ATM withdrawals.
It follows a conversation between the Greek PM and International Monetary Fund Managing Director Christine Lagarde, in which Mr Tsipras was told the lender could not provide funds to countries that had missed payments to it. Greece defaulted on an IMF loan last month.
Dutch Prime Minister Mark Rutte has said Greece must accept deep reforms if the country wants a new bailout package.
Mr Rutte said Greece must decide tonight if it wants to remain in the eurozone.
If things stay the way they are, then we're at an impasse.
There is no other choice, they must be ready to accept deep reforms.
The level of emergency credit to Greek banks has been maintained by the European Central Bank.
The ECB said today it would not change the level of emergency liquidity assistance to Greek banks from the level set on June 26.
ITV News Europe Editor James Mates said the move pushed Greek banks "closer to the edge".
Francois Hollande and Angela Merkel struck differing tones following discussions on the Greek debt crisis today.
At a joint press conference in Paris, the German Chancellor said that they were not yet in a position for further talks with Greece.
French President Mr Hollande said the door remained open for discussions after voters overwhelmingly rejected tough austerity terms set by international creditors.
But Mr Hollande warned Greek Prime Minister Alexis Tsipras he must make serious proposals.
German Chancellor Angela Merkel and French President Francois Hollande have met in Paris to discuss the Greek debt crisis.
A photograph released of the talks showed the two leaders sat round a table with advisers.
The pair are making a joint statement following the meeting.
The White House has urged eurozone nations to find a solution to the Greek debt crisis.
Spokesman Josh Earnest said it was in European and American interests that a deal be struck to allow Greece to remain in the eurozone.
Mr Earnest said it was up to Greece and its creditors to resolve the crisis, describing it as "a European challenge to solve".
German Chancellor Angela Merkel has arrived for talks with French President Francois Hollande over the Greek debt crisis.
The two leaders are meeting in Paris after Greek voters rejected an austerity package put forward by international lenders in return for a further bailout from the eurozone rescue fund.
Greek banks will remain closed tomorrow and on Wednesday, the country's bank association has said.
The group's head, Louka Katseli, also confirmed the daily limit on ATM withdrawals would remain at €60.
Greek banks were shuttered all last week after the collapse of negotiations on an aid deal and were officially due to reopen on Tuesday, before voters rejected bailout terms in Sunday's referendum.
Euclid Tsakalotos will be sworn in as Greece's new finance minister today, a presidency source has told the Reuters news agency.
Mr Tsakalotos would replace Yanis Varoufakis, who resigned following the referendum result.
"Tsakalotos will be sworn in with the political oath as finance minister," the presidency official told Reuters.
Chancellor George Osborne has told the Commons the risks to Britain are growing as the Greek debt crisis continues.
Mr Osborne said the situation could go from bad to worse and that the prospects of a happy resolution were deteriorating.
This is a critical moment in the economic crisis in Greece.
The situation risks going from bad to worse. Britain will be affected the longer the Greek crisis lasts and the worse it gets.
There is no easy way out, but even at the 11th hour we urge the Eurozone leaders and Greece to find a sustainable solution.