Deputy Secretary of State John C. Whitehead met yesterday with President Reagan, then departed for Canada and Europe on a trip aimed at persuading U.S. allies that Libya was involved in terrorist attacks at airports in Rome and Vienna last month.

Deputy White House press secretary Edward Djerejian said Whitehead is taking with him "incontrovertible evidence" of Libyan involvement in the Dec. 27 incidents, in which 19 persons were killed, including five Americans in Rome. He declined to be specific, saying the information came partially from intelligence sources.

Whitehead's 10-day trip is an effort to gain European nations' participation in U.S. economic sanctions against Libya. The allies have remained largely unconvinced about Libyan involvement, U.S. officials acknowledge, although Canada has joined the United States in banning export of oil-drilling equipment to Libya.

Norway has backed the United States in principle, and Italy, Libya's largest trading partner, has said it will ban sale of some weapons. Otherwise, the U.S. appeal for sanctions has been rejected.

Secretary of State George P. Shultz, in a news conference beamed to Western Europe, said Whitehead is carrying Reagan's "really strong conviction that international terrorism is a major problem" and "evidence of Libyan involvement in terrorism."

Shultz said "concrete evidence" exists that the airport terrorists, members of the breakaway Abu Nidal faction of the Palestine Liberation Organization, used Libyan passports.

A senior administration official said information to be conveyed by Whitehead goes beyond use of the passports and is much more detailed than anything the United States has made public.

But a State Department official, questioning Djerejian's use of the word "incontrovertible," said that "in intelligence, the rules of evidence aren't the same as in a court of law."