Most urgently, Athens is on the hook for a roughly 450 million euro loan repayment to the IMF due this Thursday.
The interior minister suggested last week the government would prioritize wages and pensions over the IMF payment, although the government later denied that was its stance.
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IMF Managing Director Christine Lagarde said in a statement after meeting with Varoufakis that she welcomed his confirmation that the loan payment due would be made on schedule.
"I welcomed confirmation by the minister that payment owing to the Fund would be forthcoming on April 9th," Lagarde said.
She said due diligence efforts in Athens and talks with teams in Brussels over the terms of Greece's bailout would "resume promptly on Monday."
The euro zone country is fast running out of cash, but the bailout extended by the IMF, European Commission and European Central Bank has been frozen until the leftist-led government reaches agreement on a package of reforms.
After a first set of planned measures failed to impress lenders, Athens offered a more detailed package on Wednesday.
But it arrived too late to be discussed at a teleconference with euro zone deputy finance ministers.
The government is hoping approval of its reform proposals will free up the remaining aid of 7.2 billion euros under its bailout and lead to the return of about 1.9 billion euros in profits made by the European Central Bank on Greek bonds.
Greece now has its hopes set on another meeting of euro zone deputy finance ministers on April 8-9, although it is unlikely that a deal could be reached by then. The next meeting of euro zone finance ministers will take place on April 24.
"It is necessary to restore the Greek economy's funding flow," Labor Minister Panos Skourletis told the Greek Ependysi newspaper on Saturday, accusing the country's lenders of taking advantage of Greece's funding limits to add pressure on Athens.
"Whether the country will meet its external obligations depends on our lenders' final political choices and stance," he said, adding that pensions and wages were not at risk.