A high Vietnamese official insisted today that Secretary of State Cyrus Vance offered in June to resume substantive talks on normalization of relations.

Vance sent the proposal to Hanoi's ambassador at the United Nations, Ha Van Lau, on June 6, according to Nguyen Co Thach, secretary of state for foreign affairs. The message was conveyed by Lau's American counterpart, Ambassador Andrew Young.

Thach said in an interview that Vietnamese and American officials held "preliminary, exploratory talks" on July 6 and July 12 at the Vietnamese U.N. mission.

Thach's comments were in response to a State Department denial that the two countries had resumed discussions about establishing relations. U.S. officials have said their talks with Vietnamese officials have been limited to such things as refugees and Hanoi's role in the ouster of the Pol Pot government in Cambodia but have not covered normalization.

Both sides have acknowledged that the two countries were close to an agreement on establishing relations in September when the United States called off further negotiations. The Vietnamese claim that the Americans did so out of concern for Washington's relationship with China, whose own relations with Vietnam have become embittered.

Thach said today that he did not want to add to the controversy but felt that he should clarify the situation.

Thach said the July negotiations were led by Ambassador Lau and Robert B. Oakley, deputy assistant secretary of state for East Asian and Pacific affairs.

He said it was his understanding that those two meetings had been expected to lead to substantive talks but there had been no development since. There are no talks going on now, he said, adding that he was uncertain what the next move would be.

The Vietnamese official said his country would not permit U.S. officials to come here as consular officers to process emigrant applications. Americans could come, he said, as members of a U.N. team dealing with refugees. State Department officials have said they are prepared to assign consular officers to a U.N. refugee group in Vietnam.

The Associated Press filed this report from Hanoi:

Thach indicated Saturday that the Hanoi government will pull its troops out of Cambodia, a move that could speed establishment of normal relations with the United States.

Thach, who has emerged as Hanoi's chief international spokesman, said in an interview that Vietnam has had difficulty providing economic help for neighboring Cambodia, which it occupied eight months ago.

Acknowledging that a long-term occupation could prove troublesome, he noted that Vietnamese forces had withdrawn after two previous occupations.

"Something unnecessary is uncomfortable," said Thach, speaking in English. "You must even take off your watch at night."

Thach gave no indication when such a pullout might take place.

State Department official Oakley told reporters in Washington Friday that normalization of relations was linked to a Vietnamese withdrawal from Cambodia.