Italian Prime Minister Silvio Berlusconi has expressed regrets over remarks comparing a German politician to a Nazi guard.
There is general uproar at Berlusconi's remarks
In a telephone call to German Chancellor Gerhard Schroeder, Mr Berlusconi "expressed his regret about the choice of this expression and comparison," Mr Schroeder told reporters.
Mr Schroeder, who had earlier demanded an apology from Mr Berlusconi, declared that for him "the incident was closed".
The Italian leader triggered uproar in the European Parliament when he suggested that Martin Schulz, a heckling German MEP who had criticised him, would be perfectly cast as a Nazi concentration camp guard in a forthcoming film.
The incident prompted an extraordinary diplomatic row between two of the European Union's biggest countries, which overshadowed the start of Italy's presidency of the European Union.
Mr Schroeder said any further steps that might be taken over the affair were the responsibility of the European Parliament.
Mr Schroeder said he told Mr Berlusconi it was in Europe's interest that the Italian presidency, which began on Tuesday,
"should now be a success" - especially because European leaders faced "a very important decision" on a European
constitution at the end of the year.
A statement from Mr Berlusconi's office confirmed that he had apologised by phone to Mr Schroeder - but he insisted that he had also been gravely offended, reports said.
The BBC's Patrick Bartlett says diplomatic relations damaged by the row will make it much harder for Mr Berlusconi to build consensus.
The fear is that a distracted and unpopular Italian presidency will not be able to give Europe the direction it needs as it prepares for the historic challenge of European enlargement, our correspondent says.
If nothing else, Mr Berlusconi has probably boosted the case for ending the EU's system of rotating presidencies, he says.
On Wednesday, Mr Schroeder's office summoned the Italian ambassador to Berlin to protest against the jibe and the Italians responded by summoning the German envoy to condemn the comments made by Mr Schulz.
The Italian leader described his remarks as an ironic joke which the translators had failed to convey.
Mr Berlusconi blamed Italy's left-wing opposition for deliberately trying to wreck his appearance in the European Parliament on Wednesday - but did not say how.
Nearly all Italy's newspapers have criticised the prime minister.
Even Mr Berlusconi's deputy, Gianfranco Fini, has joined the criticism, saying it would have been better if the prime minister had apologised.
"No accusation, however annoying, can justify the epithet of Nazi guard for a political adversary," Mr Fini said.
Mr Berlusconi rounded on Mr Schulz after the German Social Democrat MEP had criticised his business and political conduct.
Mr Schulz referred to an alleged conflict of interest between the political role of Italy's richest man and his extensive media empire.
"I know there is a man producing a film on the Nazi concentration camps," Mr Berlusconi exclaimed. "I shall put you forward for the role of Kapo (guard chosen from among the prisoners) - you would be perfect."