Long-distance phone company MCI Inc. bowed Saturday to a better offer from Qwest Communications International Inc., saying the $9.75-billion bid was superior to the pending deal MCI has with Verizon Communications Inc.

Verizon now has until late Friday to revise its $7.5-billion agreement or walk away with a $240 million fee MCI would have to pay to break the deal.

Since early February, MCI’s board has rebuffed Qwest’s efforts three times in favor of Verizon’s lower offers. Qwest is the smallest and financially weakest of the United States’ four regional telephone network owners. Verizon is the strongest and largest U.S. phone company.

On Saturday, however, MCI said it could no longer ignore the higher offer from Denver-based Qwest.

On Thursday, Qwest increased its bid to $30 a share, up from $27.50. Verizon has agreed to pay $23.10 a share.

Qwest said it was “gratified” that MCI finally recognized its bid as superior.

New York-based Verizon said in a statement that it would consider its options.

The MCI board action is a new twist in the long-running fight. The battle erupted after regional carrier SBC Communications Inc. agreed late in January to acquire AT&T Corp., the nation’s largest long-distance carrier, for $16 billion.

“This has got to be one of the most interesting if not the strangest merger dances we’ve seen in a long time,” said independent industry analyst Jeffrey Kagan, of Atlanta.