Euclid Tsakalotos said the Greek government had "done its part", adding "the ball is very much on the side of our creditors and the IMF".
Last week, talks between eurozone finance ministers aimed at unlocking Greece's next set of loans broke down.
Mr Tsakalotos said a deal at the next meeting in June was now urgent.
"There are no excuses for not getting this overall deal that the Greek economy so desperately needs in its efforts to access the markets," he said.
The meeting is aimed at deciding whether Greece has done enough to receive a â‚¬7.5bn (Â£6.4bn; $8.3bn) loan plus debt relief.
The cash is vital for Greece to avoid defaulting on a debt repayment due in July.
To secure the funds, the country has had to enact a series of economic reforms.
As part of this, earlier this month Greece's parliament approved a new package of austerity measures, including tax rises and further cuts to pensions due to be implemented in 2019-20.
Mr Tsakalotos said the government "had done its part of what it promised".
A deal is reported to be held up because The International Monetary Fund and Germany are at odds over how to help ease Greece's debts once its rescue programme ends next year.
The IMF's participation in Greece's latest bailout hinges on resolving this issue.
Mr Tsakalotos said that the eurozone would benefit from a deal that helped Greece return to bond markets again.
"There is very little point in entering a programme if the goal is not to leave the programme and leaving the programme should be not only the responsibility of the debtor country but the creditor countries as well," he added.
The Greek finance minister has warned there are "no excuses" for the country not to receive the next instalment of its multi-billion-dollar bailout.