While others of their group held a similar demonstration in Moscow's Red Square. 11 members of the War Resisters League staged a nuclear disarmament protest on the White House lawn yesterday morning after gaining access to the grounds by joining a tourist group.

Secret Service agents quickly arrested the demonstrators, nearly all of whom are veterans of the anti-war movement, and charged them with unlawful entry. They had broken free from a White House tour group shortly after exiting the executive mansion.

As startled tourists and a lone White House gate guard watched, the protesters unfurled a large banner urging nuclear disarmament and carried it across the lawn to the fountain near the Pennsylvania Avenue boundary of the grounds.

"The arms race is escalating, and it has always been the policy of pacifist groups to escalate their activities in response," said Carl Rogers, a spokesman for the New York-based group which was founded about 55 years ago.

In Moscow, Soviet police broke up a similar muclear disarmament protest, seizing the group's banner and briefly detaining 13 Westerners, including four of the seven protesters, two American correspondents and a cameraman covering the story, according to a report by the Associated Press.

No action was taken by Soviet authorities against any of the American demonstrators, who held their protest at 5 p.m. Moscow time and scattered Russian-language leaflets into the air at Red Square calling for disarmament by both nations.

Commenting on the War Resisters League's long history of opposing the neutron bomb and nuclear testing, Jerry Coffin, one of the leaders of the Moscow protest, told United Press International, "People have always told us to tell it to the Russians, so we are."

The Moscow group of demonstrators had entered the Soviet Union over the weekend on tourist visas.

In contrast to the group's treatment by Soviet police, a spokesman for the group here complained that D.C. police refused to release the 11 demonstrators on their own recognizance, choosing instead to hold them in lieu of $500 bond each.

"The Soviets sent our seven people back to their hotel rooms," said Rogers. "But here, police are keeping them in jail for holding a non-violent political demonstration. It makes you wonder."

Rogers said the nuclear disarmament movement is drawing increased civil disobedience participation by people, including many youths who never got involved in demonstrations against the Vietnam war.