The Vatican says it wants to open a "new chapter" in relations with Islam
Muslim and Vatican officials are holding historic talks in Rome to establish a better inter-faith dialogue and defuse any future tensions.
Catholic-Muslim ties soured after Pope Benedict XVI's speech in 2006, in which he linked Muslims with past violence.
The speech provoked Muslim outrage and triggered violent protests.
It also prompted leading Muslim scholars to launch an appeal to the Pope for greater theological dialogue, called the Common Word.
The manifesto now has more than 250 signatories.
Muslim leaders say protests against the Pope's speech - and also the publication of cartoons of the Prophet Muhammad in a Danish newspaper in 2005 - might have been avoided if Christian and Muslim leaders had spoken out together against such violence.
The three-day talks in Rome are being attended by nearly 60 religious leaders and scholars from each side.
The Muslim delegation is being led by Grand Mufti of Bosnia Mustafa Ceric, while Cardinal Jean-Louis Tauran heads the Vatican officials.
The meeting opens " a new chapter in the long history" of the dialogue between the two faiths, Cardinal Jean-Louis Tauran told France's La Croix newspaper on the eve of the talks.
The first two days will be taken up by discussions on God's love and loving one's neighbour, with the Pope due to meet the delegates on Thursday.
The pontiff is seeking to avoid future misunderstanding between the two religions, the BBC's David Willey in Rome says.
The Vatican is also keen to exchange opinions with Muslims about reciprocity in allowing places of worship to be built, our correspondent says.
Although many mosques are now being built in Europe, some Islamic countries, such as Saudi Arabia, still bar Christians from erecting churches there and practising their religion freely.
There are about two billion Christians in the world, just over half of them Catholics.
Muslims, who now number about 1.3 billion, recently overtook the number of Catholics worldwide for the first time.