Similar meetings have so far been held in London, Qatar and Washington, and the fourth is taking place in Sarajevo.
The Sarajevo meeting focuses on relations between Muslims and Christians and their dialogue on the common good.
The event is being held under the sponsorship of top religious dignitaries in Bosnia-Herzegovina, the Catholic Archbishop of Sarajevo, Cardinal Vinko Puljic, Serb Orthodox Metropolitan Nikolaj, and the head of the Islamic community, Mustafa Ceric.
Archbishop Williams told reporters that all believers, including Muslims and Christians, shared the same world and challenges, and that dialogue was the condition for seeking universally useful solutions.
A peace-loving vision of co-existence is the only solution for everybody, including people in Bosnia-Herzegovina, because faith must not turn into a weapon of one side against the other, he added.
The dean of the Sarajevo-based college of Islamic studies, Enes Karic, said that the West must start dialogue with over 55 million Muslims living in the western hemisphere.
"We share the same fears and hopes about how we can build bridges," Karic said.