Together, Muslim and Christian believers account for almost half the world's population.
The members of the new Catholic-Muslim Forum - 25 from each side - were attempting to establish a new dialogue after the disastrous fall-out from a speech by Pope Benedict in Germany two years ago, which was interpreted in many parts of the Islamic world as equating Islam with violence.
Some 138 Muslim leaders from around the world later wrote a letter to the Pope suggesting a new attempt to find common ground between the two religions. This week's carefully-prepared forum hosted by the Vatican was the result of that initiative.
On the third and last day of their discussions, the participants all trooped off to attend a private papal audience in the Renaissance splendour of a Vatican audience hall where Pope Benedict told them they must overcome past prejudices, and correct the often distorted images they have of each other.
The Pope did not mention his Regensburg speech.
But a professor of Islamic studies at George Washington University in Washington, Seyyed Hossein Nasr, from Iran, reminded him that throughout history "various political forces" - both Christian and Muslim - had carried out violence.
Christians in Iraq
Later in the day, the scholars and clerics assembled for a final public session in the main lecture hall of the Gregorian University in Rome. This is the Jesuit-run centre of Catholic learning where a good proportion of the world's most influential Catholic bishops have studied or lectured at one time or another in their lives.
| I think this meeting has no teeth, it is full of spin
Dr Ramsay Dass
Middle East Christians Congress president
They issued a 15-point declaration full of fine words about loving God and one's neighbour, but omitting any reference to the thorny problems of apostasy and religious conversion in the Middle East.
However, these are real issues for some of the delegates.
Taking part in the discussions was Archbishop Louis Sako, head of the beleaguered Catholic minority in Kirkuk, northern Iraq, where Islamic militants have kidnapped and killed Christians or forced them to convert to Islam. Many Iraqi Christians have chosen to flee abroad rather than convert.
"There is a difference between freedom of religion and freedom of conscience," the archbishop told me.
"In our context, freedom of religion means you can go to church and pray. But nothing else. You cannot change your religion when you are not convinced. Freedom of conscience is something else. You are responsible. In Islam there is no change of religion. They don't allow it. It is something bad.
"The Muslim scholars here have shown us their solidarity. We don't know why Christians are being attacked in Iraq. Every time I leave my country I don't know whether I shall be allowed back."
Dr Ingrid Mattson from Canada, president of the Islamic Society of North America, who also took part in the Vatican forum, explained that Christian minorities have existed in Muslim societies for centuries.
"If you look in Iraq at the mass migrations of Sunni and Shia, there is no middle class left. Unfortunately some people are trying to exploit religious hatred."
'Desire to understand'
Dr Ramsay Dass, an Iraqi medical doctor who now lives and works in Detroit and is president of the Middle East Christians Congress in the USA, sat among the few members of the public admitted to the final session of the forum.
| When you see Muslims and Christians acting as brothers and sisters it's a powerful antidote to violence and war
Cardinal Jean Louis Tauran
He claims to represent an organisation of some six million Christians of all denominations now living in America who are refugees from Muslim countries.
"Christians are being persecuted for only one reason in the Middle East - because they are Christians. They have no civil liberties, they are treated as second class citizens," he told me.
"If Professor Nasr says this is not true I should like to invite him and take him around to see the true situation. I think this meeting has no teeth, it is full of spin," he added.
The new Catholic-Muslim Forum agreed to meet again in two years' time in a Muslim country yet to be decided.
I asked Cardinal Jean Louis Tauran, head of the Vatican's Council for inter-religious dialogue, who chaired the discussions, what he thought had been accomplished in Rome this week.
"We reached a good level of mutual understanding," he said. "When you see Muslims and Christians acting as brothers and sisters it's a powerful antidote to violence and war," he added.
"What is new is the atmosphere, full of fraternity, humility and a desire to understand the other. We already have meetings with the Muslims of Egypt every two years. We believers know how to live diversity in unity. This is a talent that we can put at the disposal of society."