President Reagan and other administration officials yesterday stepped up their drive against a proposal in Congress to freeze the nuclear arsenals of the United States and the Soviet Union.

Departing from a prepared speech to the Tennessee legislature in Nashville, the president said, "Such a freeze isn't good enough, because it doesn't go far enough."

He went on to say that such a freeze at this time "legitimatizes a position of great advantage for the Soviet Union" and would provide no incentive for the Russians to reduce the weaponry in their arsenal.

"It would leave us and our allies on very thin ice, and as president I will never permit that," Reagan said.

The freeze proposal, arising from a grass-roots nuclear disarmament movement, has been introduced by Sen. Mark O. Hatfield (R-Ore.), Sen. Edward M. Kennedy (D-Mass.), 17 other senators and 122 House members. It calls for a mutual freeze on testing, production and further deployment of nuclear warheads, followed by U.S.-Soviet negotiation of major reductions on both sides.

Since last Wednesday, when Secretary of State Alexander M. Haig Jr. rejected the idea, the administration has attacked the proposal.

At the State Department yesterday, Richard R. Burt, director of the Bureau of Politico-Military Affairs, told a news briefing that the Soviet Union has continued to deploy SS20 medium-range missiles. "We are concerned and somewhat alarmed at the continuing buildup," Burt said.

Previously the U.S. estimate was that the Soviets had deployed 280 of the mobile SS20 missiles, each capable of carrying three 500-kiloton nuclear warheads. Officials have been estimating for some time that the Soviets were deploying five additional SS20 missiles per month.

According to Burt, the latest estimate is that the Russians have deployed 300 SS20 missiles. Five additional sites appear to be under construction within the Soviet Union, he added.

U.S.-Soviet negotiations on the limitation of medium-range nuclear weapons in Europe have been under way in Geneva since last December, with no report of substantial movement by either side.