Chinese troops have begun to withdraw to their own border three days after launching an invasion of Vietnam that has brought thousands of casualties, diplomatic sources here, in Bangkok and in Peking said tonight.

The reports of at least a partial Chinese pullback, which appeared to come from Vietnamese sources, followed statements quoting Chinese Vice Premier Teng Hsiao-ping as saying that the invasion was limited and would not "be extended or expanded in any other way."

Peking's official news agency continued its virtual news blackout on the fighting in Vietnam and provided no confirmation of the pullback reports.

Hanoi Radio, however, indicated that battles were continuing within the long six-mile deep strip of Vietnamese border territory where Chinese troops, tanks and aircraft have intruded. The Vietnamese report said 3,500 Chinese troops had been killed or wounded and 80 Chinese tanks destroyed in fighting in five northern border provinces.

Vietnam's ambassador to France, Vo Van Sung, briefing reporters in Paris today, said Vietnamese had suffered heavy losses of life and property, particularly in the initial Chinese artillery barrage Saturday.

He said some of the Chinese troops plunged into Vietnam's mountainous Langson area on horseback. He said some regular Vietnamese Army troops had been moved up to help support militia who were taking the brunt of the fighting on four traditional breakthrough points along the the border.

Although providing almost no details of the fighting so far, Peking has indicated that its troops would withdraw after what it called its "counterattack" had sufficiently punished Vietnam for months of harassing border raids.

Foreign analysts said they expected the Chinese withdrawal to begin as soon as they perceived a threat of intervention by the Soviet Union on behalf of its Vietnamese ally. Moscow issued a strong statement Sunday warning China to withdraw "before it is too late" and promising assistance to Hanoi.

[But U.S. officials in Washington said they have noted no withdrawal by Chinese troops, according to an Associated Press report.]

Military analysts here said the Chinese appeared to have purposely gone no deeper than six miles, despite employing a border force of up to 200,000 troops that was capable of striking Hanoi, 100 miles to the southwest. At the same time, the analysts said, the Vietnamese appeared to have held back the main body of their 30,000 to 50,000 regular army troops in the Hanoi-Haiphong area and a number of modern jet fighter squadrons.

"Vietnam probably expected the Chinese incursion to be a limited one," said one analyst. "So why get your first-rate troops chopped up when you don't have to?" Analysts estimate that Vietnam's largest body of regular army forces, 100,000 to 200,000 men, is engaged in putting down resistance by Chinese -backed Cambodian guerrillas.

A Japanese Foreign Ministry official, Kensuke Yanagiya, told the Japanese parliament Monday that Chinese troops had suspended their advance into Vietnam after penetrating six miles last night. A Japanese news agency with a correspondent in Hanoi said observers in the Vietnamese capital believed fighting had stopped by noon Monday, although Hanoi Radio reports and analysts here tended to discount that.

In a conversation with the visiting secretary general of the Organization of American States in Peking Monday, Chinese Vice premier Teng apparently gave few details of Chinese battle strategy but discussed reasons for launching the invasion in detail. Secretary General Alejandro Orfila told British correspondents in Peking afterward that Teng said China had "to take a position demonstrating that they do care... They cannot tolerate any aggression against them that could be misconstrued as indifference or weakness or just being pushed around."

Orfila said Teng made it clear "that this action will be a limited one, an action reacting to provocation that will be circumspect to take care of this particular situation and it will not be extended or expanded in any other way."

The Vietnamese, however, who have blamed the Chinese for the border tension that led to the invasion, said Peking's artillery and other weapons were taking a great toll. Hanoi Radio accused the Chinese of using unspecified chemical weapons in fighting near Dongdang in northeastern Langson Province, very near the border where Chinese artillery barrages were heavy.

Hanoi Radio said fighting was going on in the provinces of Laichau, Hoanglienson, Hatuyen, Caubang and Langson. Vietnamese forces had crippled 12 Chinese battalions, it said. Local militia forces reportedly destroyed Chinese pontoon bridges crossing the Red River, which enters Vietnam in Hoanglienson Province, thus slowing the invasion of several hundred Chinese troops at that vital point.

Vietnam's ambassador to France, Vo Van Sung, said the invasion involved a series of diversionary thrusts that eventually focused on two main targets Saturday and two more Sunday. Attacks in force came first on the Red River area and on the part of Langson where National Highway 1 cuts across hills going southwest toward Hanoi. The ambassador said Chinese forces focused Sunday on Mongcay on the Tonkin Gulf coast and on Caobang where Highway 4 heads south toward Highway 1.

During 2,000 years of repeated Chinese invasions of Vietnam and other warfare in the area, these routes traditionally have been favored by generals. Highway 4 was the scene of the first major victory by the Vietnamese army over France in 1950.

The ambassador said he did not know how many of the 21 Chinese divisions (about 200,000 troops) on the border had crossed into Vietnam.

"What is certain is that they are still pouring thousands of men across," he told correspondents in the French capital.

Travelers returning to Hong Kong from China reported seeing what they said were Chinese peasants and refugees who had been moved back from the border area to interior Chinese cities like Kweilin. Foreign correspondents based in Hanoi who had been near on the Vietnamese side of the border Saturday reported a stream of refugees heading south after the first artillery bombardment by the Chinese.

Foreign analysts said Chinese military planners appeared to be wary of the huge force of Soviet troops on their northern border. Analysts said the Soviets were on an alert that would allow them to go into action with only 24 hours' warning. About nine Soviet ships, including a missile cruiser, frigate, minesweeper and an oiler, were cruising off Vietnam, apparently gathering intelligence information. U.S. sources discounted reports of unusual American naval activity in the area.

An eventual Chinese decision to pull back all troops to the border creates the problem of defining just where that border is. Along the often mountainous 600-mile Sino-Vietnamese frontier, the lack of agreement on boundaries has apparently sparked a number of the bloody skirmishes that led to China's decision to deal a sharp blow to the Vietnamese border forces.

In an official commentary Monday, Hanoi Radio rejected a Chinese offer to negotiate the border dispute.

"This is tantamount to a robber whetting his knife to compel the house owner to negotiate the haul." the radio said.

Without any border agreement, skirmishes even after a Chinese withdrawal likely would continue. Chinese military leaders may feel more free to respond in the future with quick thrusts into Vietnamese territory, now that they have completed a major invasion.