President Reagan welcomed British Prime Minister Margaret Thatcher to the White House yesterday for a two-hour discussion of international and economic affairs in which they agreed that the Soviet proposal for an early U.S.-Soviet summit conference "needs to be carefully studied."

"For our part, we certainly have an interest in pursuing a serious, constructive dialogue with the Soviets on the issues which divide us," Reagan said in his most positive response so far to the invitation from Soviet President Leonid L. Brezhnev Monday.

In the unusually warm welcoming ceremony on the White House south lawn, Reagan emphasized what he called the "extremely grave international situation."

The president said the graves in England of Americans who died during World War II are testaments to a time when "Britons and Americans united and turned back threats to freedom. Our challenge today is to ensure that belligerence is not attempted again" because of "the false perception of weakness."

Thatcher replied: "The message I have brought across the Atlantic is that we, in Britain, stand with you, America's successes will be our successes. Your problems will be our problems, and when you look for friends we will be there."

The two conservative leaders referred to their attempts to revive flagging economies and hailed their common approach of trusting the resourcefulness and productivity of individual citizens.

"We believe that our solutions lie within the people and not the state," Reagan said. "We both place our faith not so much in economic theory but in the resourcefulness and decency of ordinary people," Thatcher said.

Reagan and Thatcher first met before either came to power and their remarks reflected the friendship they feel as kindred political spirits. The Reagan administration, however, was eager to avoid any parallels between the British economic experience under Thatcher and what is to come here under Reagan.

The inflation rate in Britain is 15 percent. It was 10 percent when Thatcher took office. Reagan inherited a rate of 12 percent. Unemployment under Thatcher has climbed from 5.5 percent to 9.3 percent. When Reagan was inaugurated last month U.S. unemployment stood at 7.4 percent.

Treasury Secretary Donald T. Regan said yesterday that mistakes by the Thatcher government had reduced its chances of successfully dealing with Britain's economic problems. Regan said Thatcher failed to cut taxes sufficiently and spent too much in an effort to increase productivity.

White House press secretary James S. Brady was quick to draw similar distinctions between the Thatcher and Reagan economic programs. He first offered reporters a White House staff-written paper listing differences between the economic situations here and in Britain. The paper was not forthcoming, but the White House surfaced a senior government official who, on condition he not be named, gave a lengthy discourse on how much blacker the economic future is for Thatcher than for Reagan.

Thatcher somewhat agreed. Reagan's "chances are greater than ours to cut government spending," she told a press conference. However, she told reporters there was little difference between her program and that of Reagan's. "He has chosen those very things we embarked on," she said.

Reagan said the two leaders, meeting first privately and then with Secretary of State Alexander M. Haig Jr. and Foreign Minister Lord Carrington and other aides, discussed problems in Europe, the Persian Gulf, Southwest Asia and Latin America.

He said they reaffirmed the two parts of the December 1979 NATO decision to moderize theater nuclear weapons and to pursue a dialogue on arms control with the Soviet Union.

Thatcher agreed with him that the Soviet proposal for a summit conference should be studied carefully, he said.

The two leaders also discussed the difficulties of combating domestic economic problems in the midst of a worldwide recession, Brady told reporters.

Reagan has made reinforcement of the traditional U.S. alliances one of the first objectives of his administration and Thatcher was the first head of a major U.S. ally to visit the Reagan White House.

She said she was honored to be invited so early in the new administration and found it "a double joy" to visit the United States at a time when her "trusted friend" is in the White House.