George Bush is proceeding cautiously in his early dealings with Mikhail S. Gorbachev, but Republican senators say the Soviet leader's troop reduction announcement is putting pressure on the president-elect to make a quick counterproposal.

Six weeks from taking power, Bush already faces the problem of how to respond to Gorbachev's dramatic declaration that he will slash Soviet military strength by 500,000 men and 10,000 tanks in East Germany, Czechoslovakia and Hungary.Gorbachev's move probably will intensify pressure in Congress for deeper cuts in the Pentagon budget and spark demands for reductions in American troops in Europe.

For the moment, Bush has put the matter on the back burner, telling Gorbachev he needs more time. "He understood that," said Bush, who still has to assemble members of his national security team and develop priorities and strategy for his administration.

While applauding the cutback plan, Bush said it does not compel the United States to do anything, because it was a unilateral move by the Kremlin.

Even with the announced reductions, Bush said, the Soviets still will have a big advantage in battle tanks, artillery and other conventional arms.

Yet, Republicans say Bush cannot let the Soviet offer go unanswered.

"It's going to heighten expectations for further progress in arms negotiations," said Sen. John McCain, R-Ariz. "It's important the Bush adminstration come forward with a counterproposal at the earliest opportunity."

Sen. William Cohen, R-Maine, said, "There's no doubt this will accelerate the need for Bush to put his team together" to formulate strategy. "It came at a time when President Reagan is not in a position to make any concessions and President-elect Bush is not in a position to make any agreements.

"It gives Gorbachev about six toeight weeks of pretty high-flying propaganda," Cohen said.

McCain and Cohen stressed that any counterproposal must address the Soviet edge in conventional forces and not allow them to expand their advantage.

Along with President Reagan, Bush spent two hours with Gorbachev at a luncheon Wednesday on Governors Island in New York Harbor. Officials described the meeting as a warm encounter where neither side pressed very hard on substantive issues.

Throughout the year, Bush has appeared more skeptical than Reagan about the Kremlin's intentions and Gorbachev's reforms, saying at one point that the Cold War is not over. Bush took a different tack last week, warmly praising the communist leader.

"There is no question that Mr. Gorbachev is a very different individual from his predecessors," Bush said after the meeting. "He is a warm human being, and people see that. He is committed to change."

Later in the week, Reagan said Gorbachev has never shown any reason to be mistrusted and, indeed, has guided the Kremlin away from its old goal of a one-world communist state.

Hard-line conservatives say Reagan is acting starry-eyed about Gorbachev, and predict Bush will be tougher.

"Reagan has bought the naive point of view that somehow Mr. Gorbachev and he can make world peace together when it is the system we are confronting, not some particular individual, and Gorbachev could be gone tomorrow," said Paul Weyrich, president of the Free Congress Foundation.