"Economically speaking, the IMF is no longer necessary for Greece's stabilisation," said Ewald Nowotny, head of Austria's central bank and an ECB Governing Council member.
"This is a problem that the EU can resolve on its own," Nowotny told Austrian daily Die Presse in an interview.
His comments came after WikiLeaks released what it said was a transcript of a phone conversation between IMF officials expressing frustration at Greece's slow pace enacting reforms.
The document published by the whistle-blowing website quoted the officials as suggesting in a March 19th conversation that Greece needed a "crisis event" to spur it into action. The IMF has yet to officially sign onto Greece's latest bailout, the third, agreed in July, making its participation conditional on Athens not backtracking on reform promises.
Leftist Prime Minister Alexis Tsipras, who last year said the IMF bore "criminal responsibility" for Greece's painful austerity cuts, wrote to IMF chief Christine Lagarde to complain.
She replied in a published letter that any speculation "that IMF staff would consider using a credit event as a negotiating tactic is simply nonsense".
On Monday Greece resumed talks on the reforms with mission chiefs from the EU, IMF and the ECB. Tsipras said he was confident the latest audit would be concluded by April 22nd.
The IMF is also pushing for EU nations to grant Greece relief on its mammoth debts, but members in the bloc, not least powerhouse Germany, are resisting this.
"Explicit debt relief is unlikely," Nowotny said. "Greece has already made massive progress."