Robert T. Thompson, a 52-year-old Greenville, S.C., attorney who on Jan. 1 became chairman of the U.S. Chamber of Commerce, said yesterday that he favors more cuts in defense spending.

Thompson said he was heartened that Defense Secretary Caspar W. Weinberger has found ways to cut his budget, but added: "I would hope he would find some more. I think there probably are other ways he could reduce defense spending in the future... without jeopardizing the very important defense buildup the president is advocating."

Weinberger announced Tuesday that he will propose reducing his department's budget authority for 1984 by $11.3 billion from levels previously proposed.

Speaking at his first press conference, Thompson said he thinks the chamber's 65-member board of directors at its February meeting will urge the president to go beyond a federal pay freeze to a freeze on federal spending.

"I think we will embrace some form of it [a spending freeze] as a way of containing the increase in federal spending," he said.

Thompson, a senior partner in the law firm of Thompson, Mann and Hutson, was elected to complete the one-year term of J. Paul Thayer. Thayer, who was chairman of LTV Corp. of Dallas, resigned the chamber post to become deputy secretary of defense.

During his brief tenure, Thayer, a firm supporter of the administration, clashed on several occasions with the chamber's president, Richard L. Lesher, over the organization's policies. Their most publicized split came last summer when Lesher led the chamber fight aginst a proposed tax increase.

Thompson's views on tax matters are more in line with Lesher's.

"Paul Thayer and I are good friends, but I disagreed with him," Thompson said. He said that "tax cuts so far haven't done much more than keep us even," but predicted that the 10 percent cut in personal income taxes scheduled to take effect in July will have a positive impact on the economy.

"I think the economy was in worse condition two years ago than any of us realized," he said. "We'll see it in full bloom before the year is out."

Thompson also said the chamber's finances are in good shape, despite an operating deficit that doubled to nearly $10 million between 1980 and 1981.

"I found the books to be completely in order, as did Arthur Anderson [the auditing firm]," Thompson said.