The talks focus on what this means for the religions and how it can foster harmony between them.
The meeting, including an audience with Pope Benedict, is the group's third conference with Christians after talks with Protestants and Anglicans in the United States over the last few months.
Tuesday's session began with a moment of silence so that the Roman Catholic and Muslim groups, each comprising 28 delegates and advisers, could say their own prayers for its success.
"It was a very cordial atmosphere," one delegate said, asking not to be named because the meeting was closed.
After introductory remarks by Cardinal Jean-Louis Tauran and Mustafa Ceric, the Bosnian Grand Mufti, a Catholic and a Muslim scholar delivered lectures on how their
faiths understand the concept of love of God.
Tauran, head of the Pontifical council for inter-religious dialogue, told the French Catholic daily newspaper La Croix on Monday that the forum "represents a new chapter in a long history" of often strained relations.
Tariq Ramadan, a Muslim delegate and Swiss philosopher, wrote in the The Guardian, a British newspaper, that dialogue was "far more vital and imperative than our rivalries over the number of believers, our contradictory claims about proselytism, and sterile competition over exclusive possession of the truth".
The Vatican was at first cool to the Common Word initiative, arguing that talks among theologians had little meaning if they did not lead to greater respect for religious liberty in Muslim countries, where some Christian minorities face oppression.
"We can only have a real dialogue if all believers have equal rights everywhere, which is not the case in some Muslim countries," said one Catholic delegate who requested anonymity.
The agenda for the closed talks reflects the different views of the two delegations. Tuesday's talks centred on theological issues proposed by the Muslims, while Wednesday's meeting will focus on religious freedom issues the Vatican wants to raise.
The Vatican delegation includes bishops from minority Christian communities in Iraq, Syria and Pakistan. Among the Muslims are converts from the United States, Canada and Britain.
The Catholic-Muslim Forum is due to meet every two years, alternately in Rome and in a Muslim country.
Christianity is the world's largest religion with 2bn followers, just over half of them Catholic. Islam is next with 1.3bn believers.