The stock market, ignoring reassurances by Reagan administration officials, fell sharply again yesterday after a major New York bank raised its prime lending rate for the second time in a week.

The Dow Jones industrial average, which plunged a record 95 points Wednesday, dropped another 57.61 points to 2355.09 in one of the heaviest trading days ever. In other financial markets, bond prices and the dollar also moved lower. {Details on Page F1.}

Most of the Dow's loss -- about 50 points -- came in the final 30 minutes, two hours after Treasury Secretary James A. Baker III met with President Reagan and later with reporters at the White House to assert that the economy "looks fundamentally sound."

Baker said the recent burst of higher interest rates contributing to the decline in stock and bond prices was not justified by the outlook for inflation.

As Baker met with the president, Chemical Bank, the fourth biggest bank in the nation, announced an increase in its prime rate from 9.25 to 9.75 percent.

No other banks immediately followed Chemical's move, which was the sixth increase this year in the prime rate. The prime, which was last raised by the banking industry Oct. 6, is used to set rates on many business and consumer loans, including variable-rate mortgages and home equity loans.

The stock market fell sharply after Chemical's action, but later recovered. Then it plummeted near the end of the session, traders said, because of selling called for by computer programs that track the relative prices of stocks and stock indexes.

Although Baker's remarks were mainly intended to help calm jittery domestic financial markets, he also went out of his way to challenge a recent trend of rising interest rates in West Germany, which he said did not conform to the spirit of recent international agreements.

His public criticism of the policies of a leading trading partner raised the question of whether cooperative agreements to stabilize exchange rates were in jeopardy.

Baker conceded that "there are some question marks out there" in the economy, citing in particular the large trade deficit, higher interest rates and nervousness in the stock market.

"But conditions do not warrant 'Apocalypse Now' worries or scenarios," he said, referring to a comment by Federal Reserve Board Chairman Alan Greenspan that "inflation expectations are overblown."

Baker added that "Over time, I think investors will begin to take those comments {by the Fed authorities} at face value."

Baker acknowledged that the trade deficit, which has been mounting, has been "slow to turn down," and was a source of anxiety in financial markets. It was a disappointingly small improvement in the trade deficit report for August that had triggered the Wednesday stock market slide.

But Baker reiterated the administration view that the trade deficit in real volume terms -- as opposed to the more frequently cited dollar value -- "is moving in the right direction." He claimed that there had been a 20 percent improvement in the past year in net exports by American companies.

The optimistic comments by Baker and Economic Council Chairman Beryl Sprinkel followed a statement issued earlier by the White House press office that it expected interest rates "to move down in the months ahead."

Baker, saying that "I am not intending to sound indifferent," suggested that rising interest rates be put in perspective. He noted that bond market interest rates are still no higher than they had been in November 1985, and are below the level of May 1984.

"Today, the prime rate is less than one half of the level that we inherited when we took office" more than six years ago, he said.

He insisted that the recent upward drift of interest rates is not justified by current or prospective rates of inflation. "Chairman Greenspan and the {Fed} board have explicitly made it clear that they think, as well as we, that these inflation expectations are overblown."

Baker refused to answer directly a question as to whether yesterday's prime rate increase would lead to another increase in the discount rate, which is the rate that the Fed charges on loans to financial institutions. "I believe the chairman {of the Fed} and his board, when they say inflationary fears are largely unjustified, or words to that effect. That's what they have recently said, as recently as this morning."

Baker noted that while the Dow's 95-point drop Wednesday was the biggest single day's decline in history in points, in percentage terms it was only 3.8 percent, and the market is still at very high levels.

Baker said West Germany's increase in interest rates was "not in accord with the spirit" of international cooperation shown at meetings of finance officials, including one at the Louvre Palace in Paris last February, when they called for stable exchange rates. But he quickly added that he did not think the Louvre accord was therefore dead.

"I have no doubt that the Louvre framework can and will accommodate further adjustments as they become necessary," Baker said. He said Bonn officials would be learning of his displeasure over West German interest rate increases for the first time through his comments yesterday.

Baker said the briefing for Reagan had been scheduled some time ago and had not been triggered by the stock market decline Wednesday. He said the briefing for the president focused on favorable economic developments that promised to extend the current record peacetime expansion, now in its 59th month.

He cited a reduction in the employment rate to 5.9 percent, and the addition of "solid jobs," at least two-thirds of them, he said, paying $20,000 a year.

He said there were no expectations that the consumer inflation rate will go higher than 5 percent this year.