A quarter of the world's bishops, angered by the ordination of openly gay bishop Gene Robinson in the United States, have boycotted the Lambeth Conference, a once-in-a-decade summit of church leaders.
"We are sorry you are not here," Williams said of the conservatives who staged their own conference last month and decided to set up their own council of bishops to provide an alternative to churches preaching what they called a "false gospel" of sexual immorality.
But Williams, performing a delicate balancing act between the warring sides, did not see the end in sight for the 450-year-old church that boasts almost 80 million followers.
"Are we heading for schism? Well let's see. If this is the end of the Anglican Communion I don't think anyone has told most of the people here," he said on the first day of business at the Lambeth Conference.
Williams decided not to invite Robinson as an official delegate to the conference, but that did not stop the American bishop from coming to Canterbury on Monday to tour stalls in the conference "market place" where lobbyists set out their wares.
Robinson, whose much photographed visit coincided with Williams' press conference, has insisted: "I am not making any attempt to attend any session which is for bishops only."
"I am not staging any demonstrations," he told Reuters before coming to Canterbury.
Asked why Robinson had not been invited, Williams said: "The problem we faced within the Anglican Communion that bishops gathering for the Lambeth Conference represent not only their diocese but their participation in the fellowship of worldwide Anglican Christians.
"Where there are bishops whose participation in that worldwide fellowship is for one reason or another questionable, that is the reason for questioning their participation," the Archbishop of Canterbury told reporters.
Williams insisted a broad Anglican church could survive.
"This isn't the end of the story and it's not that the provinces who are absent have said 'We want to pull out of the Anglican communion - this is it.'
"They have expressed grave disquiet and serious criticism which has to be responded to and engaged with in the months and years ahead," he said.
