"When dreams collide, the only solution is an honorable compromise," Dr Carey said in a sermon at St. George's Cathedral in Jerusalem. "That means seeking to understand the longings and hopes of other peoples."
Dr Carey, who served as a trustee of the Tantur Ecumenical Institute between Bethlehem and Jerusalem before becoming archbishop, is in Israel for a week for a meeting with the 36 other leading archbishops of the Anglican Church.
He expressed disappointment at Israel's recent decision to build a new settlement for 32,000 Jews at Har Homa in east Jerusalem.
"We look on with anguish as new actions on either side appear to undermine the peace process," Dr Carey told the 250 people assembled in the cathedral.
"The current crisis with regard to new settlements in east Jerusalem is just one of these."
In his sermon, he quoted from a young Palestinian's poem about his desire to "win back our homeland".
"As I read it, I realised how much I take for granted the sense of belonging and identification I find in being British," Carey said. "Can I deprive other of that right? Surely not."
Carey plans to visit the autonomous Gaza Strip on Friday and meet with the Palestinian leader, Yasser Arafat. The archbishop called on all countries and religions to help make peace in Jerusalem.Reuse content