Correction Appended
BEIJING, Sept. 19— A Vietnamese Deputy Prime Minister arrived today to attend the Asian Games beginning Saturday in the highest-level official visit here by a Vietnamese since Beijing and Hanoi fought a brief border war in 1979. Both sides said they hoped for a normalization of relations.
Relations between China and Vietnam have been gradually improving in recent years, and the arrival today of Deputy Prime Minister Vu Nguyen Giap seemed intended to take ties one step closer. In welcoming Mr. Giap, Chinese officials dropped their normal criticism of Vietnam. 

''We in China would like to see Sino-Vietnamese relations improve gradually until normalization is realized, and this is the will of the Chinese people,'' Gu Mu, a vice chairman of the Chinese People's Political Consultative Conference, told Mr. Giap at a welcoming meeting tonight, according to the official New China News Agency. 

The arrival of Mr. Giap follows an unannounced summit meeting between Chinese and Vietnamese leaders on Sept. 3 and 4, apparently in either Nanning or Chengdu in southwestern China, diplomats said. That meeting, which neither side has yet officially confirmed as having taken place, was held to discuss a settlement to the Cambodian war, but it is not clear if any major agreement was reached, the diplomats said.

Li Reported on Hand
The Chinese side reportedly was represented at the summit meeting by Jiang Zemin, the Communist Party General Secretary, and by Prime Minister Li Peng. The Vietnamese were led by Nguyen Van Linh, the Communist Party leader, and Prime Minister Du Muoi, diplomats said. 

The Communist parties of Vietnam and China were close in the 50's and 60's, and China gave North Vietnam considerable help during the Vietnam War. 

Traditional rivalries between Vietnam and China resurfaced after the United States withdrawal from Indochina, and officials in Beijing were furious when Vietnam invaded Cambodia at the end of 1978 to oust the Chinese-backed Khmer Rouge forces there. In early 1979, China mounted a brief border war against Vietnam to punish it, and although diplomatic relations were never cut, they have been strained ever since. 

China has long said that no normalization of relations is possible until a political settlement is reached in Cambodia. Nevertheless, trade has increased sharply in recent years. 

Mr. Giap, who played a key role in outmaneuvering both French and American forces in Vietnam, told reporters at the Beijing airport that the time had come to normalize relations, Reuters reported.
''The time is ripe for this,'' Reuters quoted him as saying.

Cambodian Talks Collapse
BANGKOK, Thailand, Sept. 19 (AP) - Talks between Cambodia's warring factions collapsed today over disagreements on how to bring rebel leader Prince Norodom Sihanouk onto a council seeking to end 11 years of civil war. 

The factions accused each other of sabotaging the Supreme National Council, formed last week to join members of the Vietnamese-installed Government and the three-party guerrilla coalition.
The 12-seat council held its opening session Monday at the Cambodian Embassy in Bangkok. Progress quickly stalled when the Government side rejected guerrilla demands that Prince Sihanouk be the council's 13th member and its chairman. 

The council, established under a United Nations-drafted peace plan, has six seats for the Government and two for each of the three rebel factions. The plan also allows for a 13th seat for a chairman.
Ek Sereywath, a spokesman for Sihanouk, expressed optimism the dispute would be settled before the Oct. 18 deadline for Cambodia's new credentials to the General Assembly of the United Nations. The Supreme National Council is supposed to replace the rebel coalition in the United Nations seat.