President Reagan met yesterday with his newly reappointed commission on U.S. strategic nuclear forces amid indications of increased activity in the quest for an agreement with Moscow on reducing the number of long-range nuclear missiles and bombers on both sides.

The activity occurred in Washington, where the president met for 30 minutes with his bipartisan commission, and in Geneva, where the Strategic Arms Reduction Talks (START) are under way.

In Geneva, the United States this week, as expected, offered a new draft treaty for a proposed START agreement encompassing changes in the original U.S. proposal that Reagan unveiled here last month.

But in Washington, sources said there appeared to be more activity in the START negotiations and more to the U.S. negotiating position than has been made known publicly. They declined to provide details.

After the meeting with Reagan, the six members of the 10-man commission who attended the presidential session received a more detailed briefing on START negotiations from Reagan's national security affairs adviser, William P. Clark, and his deputy, Robert C. McFarlane. It was after that session that commission members reportedly felt "there was more going on than we thought," as one source put it.

The sources said they viewed the greater level of activity and detail as a positive sign, but added that this should not be interpreted to mean that any breakthrough was near.

On June 8 Reagan announced that he had given U.S. negotiators "new flexibility" to try to reach an agreement. This involved allowing a smaller reduction in the allowed number of missiles in each arsenal, which moved the U.S. proposal somewhat closer to a Soviet proposal, and offering the Soviets alternate ways to limit the overall missile throw-weight, or destructive power, of opposing forces.

It is this proposal that was presented formally at Geneva this week. The Soviets also have recently dropped some demands involving U.S. submarine-based missiles. While the shifts on both sides are marginal and the central differences over each side's main missile arsenals remain, there does appear to be some movement in these talks.

It was also on June 8 that Reagan formally extended the life of the bipartisan commission, headed by retired Lt. Gen. Brent Scowcroft, and yesterday's meeting was the first since then.

That commission had recommended the changes in the original START position to Reagan. It also recommended deployment of 100 new multiple-warhead MX missiles and rapid development of a smaller, single-warhead missile for the future that would be less fearsome than the MX and thus hopefully less likely to be fired quickly in a crisis.

In order to get congressional approval of the MX, which the White House wants most, it accepted the arms control and small missile that Congress wants most.

Yesterday, White House officials said Reagan told the Scowcroft panel he wanted them to "monitor" the progress of all three recommendations--on arms control proposal changes, MX deployment and small missile development--and to develop their own system for doing that.

The president, officials said, also told the panel that the administration has almost finished analyzing another proposal being pushed by Congress and the commission. This involves the so-called "guaranteed build-down" formula for removing more than one old nuclear warhead each time a new one is added.