Yanis Varoufakis said that instead he wanted direct talks with eurozone leaders, to try to cancel some of the money Greece owes.
Varoufakis made the comments during a meeting in Athens with Jeroen Dijsselbloem, head of the eurozone finance ministers' group, marking the start of Greece's drive to persuade its creditors to ease the strict terms of the bailout.
The Greek minister said his country had no intention of co-operating with a mission from the EU, European Central Bank and IMF, which had been due to return to Athens.
Varoufakis gave no indication of what Greece would do if it cannot reach an agreement by a February 28 deadline, when the bailout ends.
Without the EU/IMF bailout programme, Greece's banks would lose their access to ECB funding.
The centre-right New Democracy party, which lost power in Sunday's election, said the new government "does not understand what it is about to do".
Dijsselbloem also met Alexis Tsipras, the Greek prime minister, who led the Syriza coalition to victory in Sunday's elections.
Tsipras and Varoufakis will visit London, Paris and Rome next week, Reuters reported.
Although neither France nor Italy has shown any sign of accepting the Greek government's demand to write off part of its $360bn debt, they have both previously called for a change of course from German-style budget austerity.
German Finance Minister Wolfgang Schaeuble said Berlin was open for talks with the new government about its debt, but he also made clear that Athens had to do its part.
"We need solidarity in Europe, and besides we cannot be blackmailed," Schaeuble said.
The Greek prime minister has repeatedly said he wants to keep his country in the euro but he has also made clear he will not back away from election campaign pledges to roll back the terms of the bailout.