WASHINGTON, Aug. 8 -- About 37 demonstrators were arrested here this morning after an all-night sit-in front of the White House to protest American policy in Vietnam.

Policeman who had said that "they can stay here as long as they want," when the demonstrators blocked the Northwest gate Friday, changed their minds after the protesters spread out and blocked all seven entrances to the White House.

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About half of those arrested were charged with blocking the entrance to a public building and half with failing to move when ordered to by a police officer. Police said most were released later although "a couple" were still being hold.

Hundreds of the anti-war demonstrators picketed the White House Friday while 67 others staged a sit-in at its northwest gate.

The demonstrator demanded that about 100 of their number be allowed to present to President Johnson or one of his assistants the signatures on a peace petition. A spokesman said that "nearly 7000" people have signed the petition, pledging to refuse service in the armed forces and to encourage obstruction of the American war effort.

The Rev. A. J. Muste, 30-year-old retired Presbyterian minister and a leader of the demonstration, outlined the group's demands to White House aids Chester Cooper in a 15-minute confrontation just outside the gate. "You can't have a discussion with 100 people," Cooper answered. He asked that a delegation of five people be selected to meet with him in his office.

The sit-in began at 5:10 p.m. with the 67 demonstrators who were sitting at the gate encircled by nearly the same number of policemen. Between 500 and 600 other demonstrators marched in a nearby picket line that was loosely surrounded by about 150 policemen.

None of the people sitting down was arrested. "As far as I'm concerned, they can stay here all night," commented John E. Winters, deputy chief of police. "But if the White House wants to use this gate." he said, "the White House will use it."

The White House apparently did not want to use the gate, but only a handful of demonstrators stayed to find out. At 6 p.m., the time at which the day's activities were scheduled to end, leaders of the demonstration recommended ending the sit-in. "We have made our point," said Muste. "What we have done has come to the attention of the President."

"I don't think sitting here does any good," counseled folksinger Joan Baes, who was among the sit-in demonstrators. "I don't think they are going to make any arrests, I don't think they are going to use this gate, and I don't think the President gives much of a damn," she declared.

Fourteen demonstrators continued the sit-in, and most of them were still at the gate early Saturday. They left later in the day to join-peace workshops that were conducted on the grounds of the Washington Monument, but returned Saturday night.

Earlier in the day, an estimated 1000 demonstrators braved the near 90-degree midday heat to keep a half-hour silent vigil in front of the White House. At least one man collapsed under the withering sun.

Friday's demonstrations launched a four-day program of talk and action in opposition to the war in Vietnam. The demonstration Friday was sponsored by the Committee for Nonviolent Action, the War Resistors League, the Student Peace Union, and the Catholic Worker.

For the next three days, however, the program is being carried out by a loosely-organized group which has called for an "Assembly of Unrepresented People." That group in- cludes Muste: Robert Parris. (Robert Moses), field secretary of the Student Nonviolent Coordinating Committee; Stoughton Lynd, professor of History at Yale: Russ Nixon, general manager of the National Guardian; and Carl Bloise, director of publications for the W.E.B. Dubois Clubs.

The "Assembly" will try Monday to convene itself in the chambers of the House of Representatives in order to "declare peace with the people of Vietnam." Leaders have indicated that they expert mass arrests