Incoming European Commission President Jose Manuel Barroso is hoping to defuse a row over his controversial choice of justice commissioner.
Many Socialist MEPs want Mr Buttiglione's nomination withdrawn
He is meeting European Parliament leaders in a bid to secure support for a confidence vote next week.
Several parties threaten to reject the whole 25-member Commission unless the nomination of Rocco Buttiglione for justice commissioner is withdrawn.
Mr Buttiglione sparked anger with his remarks about homosexuality and women.
During a confirmation hearing last week, Mr Buttiglione said he regarded homosexuality a "sin", and that marriage existed to allow women to have children and the protection of a male.
Last Friday, the Italian was also reported as having said single mothers were not very good people.
Mr Buttiglione later said he had been quoted out of context, and has claimed he is victim of a "hate campaign".
His supporters have also hit back with claims of bias against devout Catholics.
But his comments have incensed the Socialists, the Greens and some liberals, who say he is not fit to be justice and home affairs commissioner.
The post entails supervision of discrimination issues, including the rights of women and gays.
Speaking before Thursday's meeting with European Parliament President Josep Borrell and eight party leaders, Mr Barroso said he was "optimistic that a balanced solution will be found".
The parliament will vote on the new Commission team next Wednesday.
The BBC's Europe Correspondent Tim Franks says Mr Barroso is in a quandary.
He could move the part of Mr Buttiglione's brief that deals with discrimination to someone else in the Commission, but some MEPs have said that would not go far enough.
"We expect and demand a complete change in portfolio for Mr Buttiglione," Socialist group leader Martin Schulz was quoted by the Associated Press as saying.
Social Democrat Hannes Swoboda warned that "if Barroso and Buttiglione don't react, it is highly probable the confirmation of the Commission will be put in
Danish Socialist Poul Nyrup Rasmussen also said there was "now a risk that the Commission could be voted down next week".
Neil Kinnock, who is standing down as the British commissioner, told BBC Radio 4's Today programme that only Mr Barroso could resolve the row.
He said it was unlikely that Mr Buttiglione would "consider his position," so there should be "some form of reconstruction of Mr Buttiglione's portfolio or maybe a wider
The 268-strong conservative European People's Party - the largest in parliament - firmly backs Mr Buttiglione.
But nearly half of all MEPs are believed to be against the Barroso Commission if Mr Buttiglione is allowed to stay in his job - the 200-strong Socialists supported by the
Greens, eurosceptics and other leftists, Reuters news agency reports.
The outcome could depend on the assembly's Liberal group, the third largest. They are seen as split on whether to accept that Mr Buttiglione remains as Justice Commissioner.