Jean-Claude Juncker has accused the Greek government of misleading voters as Alexis Tsipras said its creditors were trying to “humiliate” the country.
The European Commission president said the government had not told the truth about its bailout proposals.
“I am blaming the Greeks [for telling] things to the Greek public which are not consistent with what I’ve told the Greek prime minister,” Mr Juncker said.
Mr Tsipras said the IMF bore “criminal responsibility” for austerity measures.
Demands by its lenders for more cuts were politically motivated, the Greek leader added.
Greece needs to strike a deal with its creditors before the end of June or face defaulting on payments of €1.6bn (£1.5bn) due to the IMF.
Mr Tsipras had earlier said the main factor blocking a deal were differences between its European and IMF creditors over debt restructuring.
“The big contradiction is the IMF’s presence, which wants measures and a restructuring, [whereas] the others want measures but no restructuring,” he said. “They want an a-la-carte IMF.”
He said he wanted a deal that would end talk of a Greek eurozone exit, but that “the mandate we have got from the Greek people is to end austerity policy”.
The Greek stock market fell 4.7% on Tuesday, following similar falls on Monday and last Friday.
Elsewhere in Europe, the FTSE 100 in London closed flat after falling 1.1% on Monday, while the Dax in Frankfurt and the Cac 40 in Paris both closed up 0.5%.
Meanwhile, White House spokesman Josh Earnest said that both Greece and its creditors should aim to restore the Greek economy without disrupting global financial markets.
In Germany, a senior member of Chancellor Angela Merkel’s Christian Democrat (CDU) party said that a Greek exit from the eurozone would result if Athens failed to present a convincing economic reform package.
‘State of denial’
Michael Grosse-Broemer, the CDU’s deputy floor leader in parliament, said: “In the event a solid reform package is not presented, then a ‘Grexit’ would have to be accepted if necessary.”
He said it was up to Greece to give up its “state of denial”, adding: “I’m not so sure anymore if the Greek government is really interested in averting damage for the people of Greece.”
In another development on Tuesday, the European Court of Justice ruled the European Central Bank (ECB) had not acted unlawfully in 2012 when it said it stood ready to buy government bonds.
Germany objected to the ECB’s announcement of a bond-buying programme, despite the fact it was never used, saying it contravened EU law.
The action of the ECB at the time helped to calm markets which, at the time, were being buffeted by one crisis after another.
Greece in numbers
Greece’s debt mountain
€56bn Greece owes Germany
177% country’s debt-to-GDP ratio
25% fall in GDP since 2010
26% Greek unemployment rate