For the first time in President Reagan's second term, the White House is struggling with a controversy that appears to have spun beyond its control. At issue is Reagan's plan to lay a wreath at a German military cemetery.

Several White House officials privately acknowledge that the problem never should have arisen, that mistakes were made and that they have been allowed to fester into a major embarrassment threatening to overshadow Reagan's scheduled 10-day European trip.

Six days after the announcement that the president would visit Bitburg cemetery May 5, the controversy remained unresolved yesterday as deputy chief of staff Michael K. Deaver, in response to protests by Jewish groups and veterans, searched for a Nazi concentration camp site to be added to Reagan's itinerary.

Also yesterday, 53 senators, led by Howard M. Metzenbaum (D-Ohio), asked Reagan in a letter to drop the cemetery visit. They cited reports that 30 members of Hitler's SS troop are buried there and noted "massive participation" by the SS in the Battle of the Bulge, in which 19,000 Americans died. The letter was signed by 42 Democrats and 11 Republicans.

The White House reaction to the controversy was slower than on many similar occasions. In the past, "they would have pulled the plug immediately," said one senior official who has been in the White House since the early days of the administration.

The flap also seemed out of character for a White House team that has prized symbolism in Reagan's travels and in his presidency. "It's such a loser. It's not the sort of thing they usually do," the same official said.

The official said that, if Reagan insists on going to Bitburg, the White House will have to deal with a "photo opportunity" in which television cameras pan from the president to the tombstones of Nazi SS officers.

Another senior official familiar with all of the internal discussions said there was no fast way to end the controversy when it erupted last week. He said Reagan told chief of staff Donald T. Regan in Santa Barbara late last week that he felt he had made a commitment to West German Chancellor Helmut Kohl to visit the cemetery and could not withdraw from it.

"It's not that we didn't realize that we were going to have to do something," this official said. "We recognized we had our work cut out for us. We knew it was a tough one. But we couldn't pull the plug unilaterally."

Informed officials said the episode originated when Kohl asked Reagan last year to join him in a "reconciliation" ceremony marking the end of World War II in 1945. Kohl told the president about a similar ceremony he had held last year with French President Francois Mitterrand at Verdun, site of a World War I battle.

One official said Kohl asked Reagan to visit a cemetery but did not specify one.

This official said U.S. and West German planning teams thought at first that they could find a cemetery containing American and German war dead, but could not. The search for a site led to Bitburg because of its proximity to an air base that Reagan also could visit.

Deaver, the chief White House official responsible for planning the visit, made two trips to Bitburg. At least one U.S. aide on the second trip expressed concern about the cemetery, particularly since Reagan, by that time, publicly had ruled out visiting a Nazi concentration camp, according to White House officials.

But the trip itinerary was approved subsequently by the president, Regan, the National Security Council and the State Department, officials said.

White House spokesman Larry Speakes announced the schedule last Thursday, touching off protests by Jewish groups and veterans. Rather than abandon the Bitburg visit, White House officials stressed Reagan's activities honoring the memory of victims of the Holocaust in the United States and waited a few days to see if the protests would stop.

The protests continued this week even after Reagan decided to schedule a concentration camp trip.