President Reagan bowed to strong lobbying by Canadian Prime Minister Brian Mulroney yesterday and acknowledged for the first time that acid rain, threatening the environment on both sides of the border, is caused by man-made pollution.

During their joint appearance at the White House, Reagan said he fully endorses a January report on acid rain by U.S. and Canadian special envoys.

It calls for the United States to implement a five-year program, with $2.5 billion provided by government and $2.5 billion by industry, to develop technologies to combat it.

Reagan had resisted Canadian pressure to join in seeking ways to deal with acid rain, saying more research was needed to determine its cause. Privately, he had expressed disagreement that the problem was man-made, insisting that forest fires were to blame.

Reagan hinted yesterday that he still harbors doubts. He said "serious scientific and economic problems" remain to be solved.

But he was unequivocal in endorsing the year-long study by the special envoys, former U.S. transportation secretary Drew Lewis and former Ontario premier William Davis, that said man-made pollutants "contribute far more to acid rain in the United States than natural sources."

Reagan made no commitment, however, to strict government controls to reduce sulfur and nitrogen oxide emissions from coal-fired power plants in the Midwest. White House spokesman Larry Speakes said that was being studied by the Environmental Protection Agency.

The White House also left unclear how the administration would provide funding to back Reagan's promise to Mulroney.

Noting that the federal budget allocates about $400 million for a "clean coal" program over the next three years, Speakes said the president is committed to finding the rest of the money.

"How that comes has not been determined," Speakes said.

Mulroney, pressed by Canadians to gain concessions on the issue during his two days of talks here, called Reagan's statement "an essential first step" toward solving a problem "that has bedeviled our relationship for far too long."

The Canadian government had hired private lawyers to lobby for Reagan's endorsement of the envoys' report. Negotiations about language in Reagan's statement and Speakes' subsequent remarks continued until late Tuesday.

"This is a front-burner issue," Mulroney told reporters after he left the White House yesterday. "This is not going to go away until it is solved . . . . Long after it is no longer fashionable to discuss Nicaragua in Washington, we will be discussing the environment. You can be certain of that."

Reagan and Mulroney also approved a five-year extension of the North American Aerospace Defense (NORAD) agreement. To calm concern in Canada, Speakes said later that the program was not connected to Reagan's Strategic Defense Initiative, the space-based missile-defense system often referred to as "Star Wars."

At the Canadians' request, Speakes reiterated the administration commitment to the 1972 U.S.-Soviet Antiballistic Missile treaty. "The United States is pledged to abide by the ABM treaty until we say otherwise," he said.