Shares in Mellon Bank Corp. continued to slip amid tepid trading on Tuesday, as markets prepared to close for a day in observance of the death of former president Richard M. Nixon.

Mellon stock was off by as much as $1.125, before bouncing back to close at $56.125, off 62.5 cents.

Analysts attributed the decline to profit taking following a price run-up that peaked at $59.875 in intraday trading on April 18, the day before earnings were announced. In addition, investors may have been concerned about the impact of the pending acquisition of Dreyfus Corp. - a matter of sharp debate among bank stock analysts.

Brent B. Erensel of UBS Securities said the investor skittishness over a recent decline in the the value of Dreyfus equity funds and an increase in the Dreyfus' expenses "might be misplaced." He argued that the merger presents opportunities for improved efficiencies that makes Mellon stock "a great way" for investors to buy into a fiduciary company at a low price.

James M. Schutz of Chicago Corp. said the acquisition would put Mellon in the same category as Northern Trust Corp. and State Street Boston Corp. Those banks trade at 12.8 and 14.4 times earnings, respectively.

Mr. Schutz said Mellon is trading at 9.3 times his 1994 earnings estimate of $6, making his $67 price target seem conservative.

On the other side in the debate is Christoph M. Kotowski, of Oppenheimer & Co., who gives Mellon a neutral "market performer" rating. He said he doubts the bank contemplates the kind of shift in its mix of businesses that would be needed to become the kind of high-multiple asset management company the other analysts predict.

In other market action, shares in First Interstate Bancorp rose sharply to $77.125, up $1.125 on the day.

Weighing in favor of the stock were statements by the Los Angeles company that it will have no loan loss provision this year, its target of 18% to 20% return on equity, a 10% stock buyback, a 50% increase in the dividend to $3.00 per share, and a plan to cut the expense ratio to 58%.

Sandra J. Flannigan of Merrill Lynch & Co. said the uptick might reflect buying being triggered at $75. Ms. Flannigan said Merrill is urging clients to add to their position in First Interstate at that price, which the stock reached late last week.

Based on her earnings forecast of $10.75 for 1994, Ms. Flannigan said First Interstate's stock price could reach $93 by the end of the year.

First Interstate stock is "continuing the good movement it had before the market convulsed," added George Salem, of Prudential Securities Inc.

"This is a company with stockholder welfare written all over it," Mr. Salem said. "It has been volatile, but it always seems to come back. I think it's one of the most persuasive stories in bank stocks."

Bank stocks were mixed, with smaller banks generally outperforming the bigger ones.

The Dow Jones industrial average fell 6.24, to 3699.54.

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