Thousands of South Vietnamese ground troops, accompanied by American advisors and tactical air support, surged across the Cambodian border 34 miles northwest of Saigon yesterday morning.

The crossing followed last week's 12-mile penetration by 5000 South Vietnamese along 30 miles of the border.

Allied Headquarters stated early this morning that 332 "enemy soldiers" were killed in the first day of the operation. Spokesmen said that American and South Vietnamese bombers killed 300 of these, and that the South Vietnamese suffered three dead and 51 wounded.

The ostensible purpose of the South Vietnamese operation was to provide support for the right-wing military regime in Cambodia which toppled the neutralist government of Prince Sihanouk six weeks ago.

The military junta-which received diplomatic recognition from the United States government almost immediately after its inception-has lately come under sharp attack from insurgent forces within the country, about half of which are reported to be Viet Cong and North Vietnamese.

Supporters of American involvement in the South Vietnamese action, including the Pentagon, claimed yesterday that this involvement is a limited gesture, in line with the Administration's "Vietnamization" strategy and its policy of phased U. S. military withdrawal from Southeast Asia.

But critics of U. S. involvement in the operation yesterday denounced the move as an escalation of American military commitment in Southeast Asia.

Sen. J. William Fulbright (D-Ark.) called the American involvement "a great mistake," and Michael Mansfield (D-Mont.), Senate Majority Leader, termed it "the first step in the wrong direction."

Moratorium Committee

Organizers of the Harvard Moratorium Committee said yesterday that they are reconsidering their decision to disband. "The Cambodian thing changed the picture entirely," Steven E. Heagan '71. a coordinator of the committee, said last night.

When news of the invasion reached the New York Stock Exchange, averages declined four points in a frenzy of panic. But after the initial shock, they resumed their upward swing and rose rapidly to 13 points above Tuesday's level in one of the market's best sessions this year.