President Reagan last night tried to quiet the crisis of the financial markets by declaring at a nationally televised news conference that he will negotiate "as soon as possible" with congressional leaders on a package to reduce the federal budget deficit.

While the president backed away from previous vows to veto any tax boost and refused to give a definitive position in advance of the negotiations, he made clear that he remains philosophically opposed to tax increases, particularly on income. Reagan also reiterated his view that the economy is fundamentally sound, despite the panic selling that began with a record stock market drop Monday.

"This is purely a stock market thing, and there are no indicators out there of recession or hard times at all," the president said.

It was unclear immediately afterward whether Reagan's performance had accomplished its goal of reassuring Wall Street. Peter Cohen, chairman of Shearson Lehman Brothers, called the session "very, very disappointing" and said the president showed insufficient understanding of the stock market and the economy. But Peter Buchanan, president of First Boston Corp., said Reagan's remarks displayed "the right attitude."

Congressional leaders of both parties welcomed the president's remarks, saying his willingness to negotiate a budget accord with no preconditions offers an opportunity to break through the budget stalemate and send a positive message to the markets. ". . . He sincerely wants to negotiate and achieve a package we all can support," said Senate Majority Leader Robert C. Byrd (D-W.Va.).

Before the news conference, the White House had reacted to another day of slumping markets by letting it be known that Reagan would name a high-level administration team to negotiate with Congress on a deficit-reduction package. Reagan did so at the news conference, saying, "I'm putting everything on the table -- with the exception of Social Security -- with no other preconditions. And I call on the leaders of Congress to do the same."

He named Treasury Secretary James A. Baker III, White House chief of staff Howard H. Baker Jr. and budget director James C. Miller III to represent the administration in the negotiations with Congress. The president also announced he will name a panel to examine Wall Street procedures. It will be headed by investment banker Nicholas Brady, a former Republican senator from New Jersey and a close friend and confidant of Vice President Bush.

Reagan also announced that the final deficit figures for fiscal 1987 had fallen from $221 billion in 1986 to $148 billion, making the deficit about $5 billion lower than had been expected.

As anticipated by the administration officials who spent hours intensely preparing Reagan, questions about the economy dominated the first news conference that the president has held in this country in seven months. Reagan alluded to his long inaccessibility by quipping at the opening of the news conference, his 42nd, "Well, it just seems like yesterday."

The president also responded to several foreign policy questions and strongly defended continued deployment of U.S. naval forces in the Persian Gulf. He dismissed congressional calls for invoking the 1973 War Powers Resolution in the gulf conflict and said Iran would be "running a great risk" by attacking American flagged tankers in the gulf.

"We're not there to start a war," Reagan said. "We're there to protect neutral nations' shipping in international waters that under international law are supposed to be open to all traffic."

Two themes dominated Reagan's discussion of economic conditions. The first was his view that the nation's economy has not been basically shaken by the ups-and-downs on Wall Street. The second was that he remains convinced that tax increases, particularly income-tax hikes, are undesirable despite his willingness to negotiate with Congress on "a procedure for deficit-reduction discussions that will be productive and constructive."

Reagan turned aside several attempts to pin him down on exactly what he might accept, saying that it would be unwise of him to make such a commitment in advance of the negotiations.

"This situation requires that all sides make a contribution to the process if it is to succeed and that a package be developed that keeps taxes and spending as low as possible," the president said in his opening statement.

While saying in the statement that "we shouldn't assume the stock market's excess volatility is over" and acknowledging that this poses a "challenge" for the White House and Congress, Reagan minimized the importance of the tumult in his answer to the first question about the economy.

"I think this was a long-overdue correction. And what factors led to its kind of getting into the panic stage, I don't know," Reagan said.

Responding to other questions, Reagan blamed Congress for a half-century of deficit budgets and for what he claimed was congressional failure to give serious consideration to his proposals to reduce deficit spending. But the president did not resort to the provocative denunciations of all taxes he has made in his political campaigns. In 1984 Reagan declared that a tax increase would become law only "over my dead body."

Despite his attempt to take a more conciliatory tone, Reagan did not attempt to conceal his skepticism about the desirability of any tax increase.

"I have not changed my opinion about ever accepting a tax that will have a deleterious effect on the economy -- and most tax increases do," he said.

The president's budget, rejected earlier this year by Congress, contained about $6 billion in actual new taxes, the bulk of it from increased tax collections and by extending Medicare taxes to all state and local government employes.

That budget contained another $16 billion in revenues from asset sales, privatization of government services, user fees and credit reform.

On other issues, Reagan said he did not know the dates or the agenda for the summit this fall with Soviet leader Mikhail Gorbachev. U.S. officials said yesterday that the dates could be announced today in Moscow, where Secretary of State George P. Shultz has been meeting with Soviet officials. The summit is expected to be held here in late November, but Reagan said it also "would be kind of nice to invite" Gorbachev to visit his ranch northwest of Santa Barbara, Calif.

Reagan also defended his nomination of Judge Robert H. Bork to the Supreme Court and said the highly charged confirmation process is "totally out of line with what the procedure should be." The Senate is expected to reject Bork formally when it votes today.

The president said the qualifications of Bork's supporters are "far superior to most of the people who were against him" and said he will "try to find somebody that is as qualified in the same way" as Bork.