The Senate began debate yesterday on a bill to establish a new basis for American relations with Taiwan as Carter administration officials lobbied intensely to head off amendments not to their liking.

The administration, it was learned, was acting in part on expressions of "grave concern" from the Peking government about the shape of the Taiwan legislation now nearing final passage in both the House and Senate. The Chinese ambassador in Washington, Chai Zemin, has expressed this concern to Secretary of State Cyrus R. Vance, according to informed sources.

The first votes yesterday on amendments to the bill indicated that the amministratin enjoyed a comfortable margin of support, but senior administratuon officials expressed concern that one amendment to be offered by Sen. Charles H. Percy (R-Ill.) could disrupt both the legislation and the process of normalization of relations with China.

The Percy amendment is expected to come up for a vote sometime today, though that is not certain. It would declare that any threat to Taiwan would be considered a threat to the "security interests" of the United States.

In the semantic minuet that characterizes debate over the Taiwan legislation, the phrase "security interests" is said -- by administration officials and supporters -- to invoke the specter if not the substance of America's mutual security treaty with Taiwan, which the United States now plans to abrogate.

On that basis, they argue, the Percy language would contradict the terms of the U.S. rapprochement with the Chinese government in Peking, and is therefore unacceptable.

Whether it is indeed unacceptable is open to question. The Chinese ambassador, sources said, expressed "grave concern" to Secretary Vance over the language approved by the Senate Foreign Relations Committee, which says a threat to Taiwan would be considered "a threat to the peace and security of the western Pacific area and of grave concern to the United States."

But there were apparently no threats from the Chinese not to accept this language. Ambassador Chai also expressed his concern to Sen. Frank Church (D-Idaho), chairman of the Foreign Relations Committee, but an aide to Church said it was not a strong expression and contained no threat.

President Carter has said that the United States retains the right to go to war to protect Taiwan, an assertion that strikes some senators as stronger than the Percy amendment by a good deal.

But as several senators pointed out in yesterday's floor debate, appearances seem more important than substance in this entire discussion.

Sen. Gordon Humphrey (R-N.H.), for example, argued that the new U.S. office in Taiwan should be called a "liaison office" -- the name of the U.S. mission in Peking until full diplomatic relations were established. The pending legislation calls this office "the American lnstitute on Taiwan."

This institute is supposed to maintain "unofficial" relations with Taiwan. Humphrey noted that it will be manned by U.S. government employes "on leave" from their normal duties -- but still considered members of the Foreign Service pension program.

An amendment offered by Humphrey to rename the institute a liaison office was defeated 57 to 38.

Another amendment offered by Sen. Bob Dole (R-Kan.), to eliminate the euohemism "the people on Taiwan" from the bill -- referring instead simply to Taiwan -- was defeated 62 to 33.

Administration officials were concerned yesterday that Sen. Howard H. Baker Jr. (R-Tenn.), the minority leader, had apparently decided to vote for the Percy amendment. Baker had earlier supported the Foreign Relations Committee's language, but had reserved his position on Percy's proposal.

Deputy Secretary of State Warren Christopher met with Baker and Percy to urge them not to press the amendment, which Christopher said was potentially damaging to Sino-American relations. Baker said later he wasn't convinced, but then left town for speaking engagements from which he is not planning to return until Monday.

The Senate last night debated the constitutionality of Carter's decision to abrogate the defense treaty with Taiwan without a concurring vote of the Senate, an issue that is the subject of a lawsuit brought against Carter by Sen. Barry Goldwater (R-Ariz.) and two dozen other members of Congress.

Sen. Harry F. Byrd Jr. (Ind.-Va.) offered a "sense of the Senate" resolution saying that treaties should be abrogated only with Senate concurrence. It will be voted on at noon today.