President Reagan, seeking personally to dispel any notion here and abroad that he is somehow hesitating on arms control, said yesterday that he is "determined" to reach agreement with the Soviet Union and vowed to "stay at a table negotiating as long as there is any chance at all of securing arms reduction."

The president, in a 20-minute, nationally televised session with reporters in the White House briefing room, called reduction of stockpiled nuclear arms "the most important problem facing this generation."

He said that his defense buildup in the past two years has given the United States the "leverage" to get Moscow to bargain seriously, so that "now we're in a position to get somewhere, and I'm determined that we shall."

The president's remarks were the third time in as many days that either he or Secretary of State George P. Shultz took special steps to convince critics and skeptics that the administration is sincere in seeking agreements and has its policies under control.

The efforts at reassurance come after a major shake-up in the U.S. arms control agency and a flurry of arms control speeches and other comments recently from the new Soviet leader, Yuri V. Andropov.

Andropov's statements have made a big splash in the West and, in the view of many U.S. and allied officials, are aimed at splitting the allies away from the U.S. position in the Geneva arms talks. The United States is insisting that it will begin deploying 572 new intermediate-range missiles in Europe in December to balance about 600 Soviet weapons already in the field unless an arms control agreement is achieved before then.

As that deployment draws near, protests against it by various groups in western Europe are expected, and the administration has been seek- ing some way to respond to Andropov and soften the demonstrations.

Along these lines, Reagan yesterday stressed that "we will consider every serious proposal" submitted by the Soviets and expressed great confidence in the U.S. negotiator at the talks on European-based missiles, Paul H. Nitze.

Reagan's expression of support for Nitze, officials said, was also meant for the allies who were clearly shaken by Reagan's firing on Wednesday of Eugene V. Rostow as director of the U.S. Arms Control and Disarmament Agency. Reagan described that action yesterday as not a policy shift but mostly an effort to get a "streamlined team" that can act quickly and "get results in the Geneva talks."

The president said no one should believe there was disarray in the administration because of Rostow's firing or because of what they read about it. But yesterday, European papers, according to news agency reports, were filled with editorials linking the firing of Rostow, who had pushed for some flexibility in negotiations, to supposed Reagan chilliness toward the idea of arms control.

Although Reagan previously has said that there is perhaps a 50-50 chance of reaching arms agreements this year, yesterday he declined to speculate on whether an accord is possible by the end of his current term in office, which is two years away.

The president said both the leverage provided by a military buildup and determination "are essential to success in arms control." To back up this formula, he suggested that "some people" argue for "unilateral disarmament . . . in the hope that our example will lead the Soviets to cut" their forces.

Reagan said such an approach doesn't work and had been tried by President Carter when he "decided to cut the B1 bomber perhaps in the expectation that the Soviets would cut back on their bomber programs."

Actually, Carter cancelled the B1 because he believed the bomber would not get through Soviet air defenses, and decided instead to start secret work on a more advanced bomber known as "Stealth" and to step up production of air-launched cruise missiles so that bombers would not have to fly through those defenses.

To back his claim that Moscow has incentive to bargain only when the United States is moving ahead with new weapons projects, Reagan also cited the 1972 treaty limiting anti-ballistic missile defense systems, which was achieved "when it became clear that we would go ahead with the deployment."

Reagan, under questioning, also rejected the idea of considering any summit meeting with Andropov until there is some feeling about whether the next round of arms control talks, which begins later this month in Geneva, is leading to any progress.

Andropov has called for a summit, something that also has appeal among U.S. allies in Europe.

Andropov met recently with Hans Jochen Vogel, the Social Democratic party candidate for chancellor in West Germany. It was reported on Thursday that Andropov had expressed to Vogel a willingness to discuss not only reduction of missiles but also of missile warheads in the Geneva talks on European missiles.

This is potentially significant because the Soviets have many more warheads on their missiles, and it could imply a willingness to accept some new U.S. weapons deployments. There was no clear public response to this in Washington yesterday. Privately, administration officials expressed skepticism over the reports and suggested that Vogel was in the midst of a political campaign and being used by the Soviets.

Officials said that whatever Moscow was officially proposing would have to be made clear at the Geneva talks.

Meanwhile, there were indications from some officials here yesterday that more reorganization is going on quietly in the government and that it seemed to be linked to the growing role of the State Department and Shultz in arms control.

Officials say there is some mystery and perhaps irony attached to Shultz's role. Among advocates of arms control, the increasing involvement of Shultz in the issue is viewed as a hopeful sign that a reasonable compromise with Moscow can ultimately be worked out. This is because Shultz is close to the president and is viewed as more moderate than some of Reagan's advisers.

Yet even very senior officials say they do not know Shultz's views on the subject, or even if he has any.