Senior Reagan administration officials and congressional leaders, meeting in an atmosphere of financial crisis and heightened political expectations, yesterday began what they described as substantive negotiations on a plan to reduce the federal deficit.

The initial two-hour session on Capitol Hill yielded a "conceptual agreement" that Congress and the White House should aim for at least a $23 billion reduction in the federal deficit this fiscal year that should come from "meaningful" spending cuts and tax increases that would continue to have a deficit-reducing impact in future years.

"We're just starting, but everybody had the right spirit," said Sen. Lawton Chiles (D-Fla.), the chairman of the Senate Budget Committee and one of 14 congressional negotiators who met with Treasury Secretary James A. Baker III, White House chief of staff Howard H. Baker Jr. and Office of Management and Budget Director James C. Miller III.

"I consider it progress," Chiles said.

He said the first session of the budget summit lawmakers had been seeking for months focused on the necessity of "meaningful" cuts in the deficit totalling at least $23 billion.

Other participants said the session was devoted to setting "ground rules" for additional working meetings scheduled to resume this morning. Lawmakers described a "cordial" atmosphere largely free of the partisan rancor that has marked this year's prolonged budget debate, a sign of how the stock market upheavals of the past two weeks may have changed the capital's political dynamics.

"We're talking seriously and we've set a tough agenda for ourselves," Sen. Pete V. Domenici (R-N.M.) said.

Rep. Silvio O. Conte (R-Mass.) said the talks had gotten off to a "good start," comparing the meeting to the start of a "heavyweight boxing match, everyone is sparring but no blows have been hit."

Yesterday's meeting -- around a crowded table in the Senate's Lyndon B. Johnson Room began amid pledges from both lawmakers and administration officials that the panic on world financial markets demands a nonpartisan search for a significant, multiyear deficit reduction package that would revive confidence in the nation's economy.

"It is time to put aside partisan rivalries and work together for our nation's future," President Reagan said in a written statement issued by the White House.

The stock market plunge of the last two weeks, Reagan said, "has alerted us of potential dangers on the economic horizon. Anyone who doubted that these threats to our future growth were serious should have been set straight in the last couple of weeks."

Reagan's statement yesterday followed comments he made Monday suggesting that the stock plunge was merely the result of a market "correction" rather than a harbinger of more serious economic problems.

Administration officials and lawmakers from both sides of the aisle said that the goal of the talks should be a blend of spending reductions and higher taxes that would yield, at a minimum, a $23 billion reduction in the deficit in the current fiscal year that is not dependent on one-time measures such as sales of federal assets.

Wall Street is demanding that "we have to do something real, and no smoke and mirrors," said Sen. J. Bennett Johnston (D-La.), one of the 14 congressional negotiators.

In an earlier session with Republican senators, according to Sen. Mark O. Hatfield (R-Ore.), the Treasury's Baker said the administration is willing to agree to higher taxes once it establishes that Congress is ready to restrain spending. Hatfield said Secretary Baker also indicated that the White House would like to achieve a multiyear program that yields more than $23 billion savings, which would occur anyway because it is required by the nation's balanced budget law.

Hatfield said James Baker reported that the administration is not open to increases in tax rates for either individuals or corporations, but has not ruled out increasing taxes on fuels, tobacco or alcohol.

"We're beyond the quick-fix stage," Hatfield said. "This has to be a truly bipartisan effort."

At their meeting, Republican senators also discussed a freeze on entitlement program spending except for Social Security. "We've reached a whole new political environment," Hatfield said. "People are willing to look at all options."

Meanwhile, House Speaker Jim Wright (D-Tex.) listed a number of "basic principles" that he said would guide House Democrats on the congressional negotiating team.

Wright said that House Democrats regard a $23 billion savings in the first year as "just a step" and that every effort should be made to wring additional reductions in the nation's deficit -- which last year totaled $148 billion -- from the talks. The speaker also said that the package should not rely on "quick fixes, illusory savings that create a deceptive appearance."

"We will be seeking a consistent, steady, multiyear program to the extent that we can," Wright said.

Wright said the "acid test" of the administration's seriousness would be its willingness to accept at least $12 billion in higher taxes, the amount the House will vote on Thursday when it takes up budget legislation.

Johnston said that most Senate Democrats "would like to do more than $23 billion," but conceded that surpassing that goal in the first year would require measures such as asset sales.

"There is sentiment for a minimum of $23 billion and more than that on a recurring basis," Johnston said.

A number of other lawmakers, however, went to considerable lengths to dampen expectations of what the talks may achieve, saying failure to accomplish what was anticipated could send further tremors through Wall Street.

"It would be a mistake to raise expectations too much," said Sen. Lloyd Bentsen (D-Tex.), chairman of the Finance Committee. "The market is being driven as much by psychology as by substance."

"Success is achieving $23 billion by the agreement of both parties," House Majority Leader Thomas S. Foley (D-Wash.) added. Domenici, the ranking Republican on the Senate Budget Committee, indicated that he would be satisfied with an initial year reduction of $23 billion as long as there is an accord for a two-year program that would continue to reduce the deficit in 1988.