U.S. Ambassador to the United Nations Andrew Young's 10-nation Caribbean tour began today with an unusual twist: His host, Prime Minister Michael Manley, was off visiting another country.

Manley's failure to be on hand to greet Young was not a sign of rudeness. Instead, Young had insisted that the Jamaican leader go to Bogota. Colombia, to take part in discussions on the most pressing issue in U.S.-Latin American relations - an agreement on the Panama Canal.

Earlier this week, President Carter sent Gen. Omar Torrijos, who controls Panama, a detailed U.S. proposal for returning sovereignty over the canal to Panama. Torrijos then asked Manley and four other influential hemispheric leaders - the presidents of Colombia, Venezuela. Mexico and Costa Rica - to meet with him in Bogota today to discuss the U.S. proposal.

Manley first rejected the invitation. saying he had to remain in Jamaica to receive the American visitor. Young told reporters during the flight from Washington to Jamaica. however, that Panama's ambassador to the United Nations had told him that Torrijos considers it vitally important to obtain Manley's views on the proposed canal agreement.

Young said he contacted Jamaican Foreign Minister P. J. Patterson and urged that Manley go to the Bogota meeting. The prime minister is scheduled to return to Jamaica late tonight.

"I think this is an indication that the meeting in Bogota is not to attack the United States but to go get key leaders of the region together for serious discussion and try to reach some consensus on the canal issue," Young said.

He refused to discuss details of the U.S. proposal. State Department officials traveling with Young said that, while a number of points remain unresolved, they feel that the Carter administration and Panama are close to agreement on the canal's future status.

Young's mission is part of a Carter adminstration attempt to forge a new policy of priority attention to the Caribbean.

The country's recent relations with the United States have been somewhat strained because Manley's policies - characterized by nationalism, outspoken identification wih the Third World and activist government intervention in the economy - are regarded in some quarters as hostile to American interests.Last year, there were charges here that the Central Intelligence Agency was trying to "destabilize the Manley government.