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 has said that the lenders wanted to raise VAT on electricity.
Other Greek ministers have criticised suggestions to increase sales tax on medicines.
However, Mr Juncker said: "I'm not in favour, and the prime minister knows that, ... of increasing VAT on medicaments and electricity. This would be a major mistake."
"The debate in Greece and outside Greece would be easier if the Greek government would tell exactly what the Commission... are really proposing," he added.
Greek finance Minister Yanis Varoufakis claimed that EU proposals did include VAT increases: "Juncker either hadn't read the document he gave Tsipras - or he read it and forgot about it."
Mr Tsipras said on Tuesday that the EU and International Monetary Fund wanted cuts to pensions and tax rises to "humiliate not only the Greek government... but humiliate an entire people".
The IMF bore "criminal responsibility" for austerity measures that had plunged the Greek economy into recession, he added.
Greece needs to strike a deal with its creditors before the end of June or face defaulting on payments of €1.6bn (£1.1bn) due to the IMF.
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.
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.