North Fork Bancorp’s board put off a decision Tuesday on whether to drop a $1.9 billion cash-and-stock offer for rival Dime Bancorp.

The North Fork board said it suspended its meeting after learning Monday that the Federal Reserve Board has scheduled a consideration of North Fork’s possible purchase of Dime for a meeting today.

North Fork said its board will reconvene Thursday to decide whether to extend its offer for Dime or abandon the effort, according to a statement issued by North Fork, which is based in Melville, N.Y.

A spokesman for Dime declined to comment on the development.

This month, North Fork chairman John Adam Kanas said his company needs to make up its mind soon about Dime. “It’s time to make some meaningful decisions,” he said then.

If North Fork pulls out of its six-month pursuit of Dime, as some have predicted, the company could launch a stock buyback program and later gear up for a renewed pursuit of Dime, analysts said.

“I think it’s clear that acquiring Dime, at or near the terms they’ve proposed, would be very beneficial for North Fork,” said Kevin Timmons, an analyst at First Albany Corp. “Right now it’s hard not to say that they wouldn’t try it again.”

North Fork embarked on a campaign to acquire Dime back in March. Since then, tension between the two companies has intensified, with Dime digging in its heels.

The battle between Dime and North Fork became especially heated during the summer when the two companies issued dueling press statements, and at one point North Fork announced a plan to nominate its own slate of director candidates for the Dime board. Dime called the move “grandstanding.”

North Fork’s offer for New York-based Dime was successful in one way. It effectively killed Dime’s merger agreement with Hudson United Bancorp of Mahwah, N.J.

In July Dime was energized when it won the backing of the New York investment firm Warburg Pincus Equity Partners, which agreed to free up $238 million so that Dime could buy back its shares from investors.

Dime has launched a repurchase program, aiming to buy as many as 13.6 million shares of its stock through a Dutch auction paying a per-share price of $16 to $18. But that effort, which after a rally in Dime shares left the offer price below market levels, has attracted only about 275,000 shares. This meager progress is leaving Dime to consider taking the stock buyback into the open market if the auction fails. Its shares are trading at about $21 on the New York Stock Exchange.

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