NEW YORK (AP) _ AMF Inc. has agreed to be acquired by Minnesota investor Irwin Jacobs' Minstar Inc. after Minstar agreed to sweeten its offer for a controlling interest in the leisure and industrial equipment maker, the companies announced late Friday.

The agreement came a little more than a month after AMF's board had urged its shareholders to reject an earlier offer from Jacobs.

Under the new merger plan, a wholly-owned subsidiary of Minstar would increase its cash tender offer for up to 12.5 million shares of AMF common stock to $24 a share from $23 a share.

That would give Minstar more than half of AMF's 26.3 million shares of common stock outstanding, at a cost of about $300 million.

The merger agreement was approved by the boards of both companies, and the AMF board recommended that its shareholders tender their shares to Minstar under the new tender offer which will expire at 5 p.m. July 8.

Minstar had earlier offered to buy up to 12 million shares at the $23 price. Minstar had disclosed on April 17 that it held 780,000 shares of AMF and options to acquire 1.2 million additional shares.

AMF's board had rejected the earlier offer, however. A federal judge issued a preliminary injunction against AMF earlier this month, preventing it from adopting a plan to thwart Minstar's bid.

In their announcement on Friday, the companies said that as soon as practicable after the expiration of the amended tender offer and approval by AMF's shareholders, a subsidiary of Minstar will be merged into AMF.

The announcement said under terms of the merger, the stockholders of AMF other than Minstar will be given $18.25 principal amount of AMF's 10 percent senior subordinated debentures due 1995 guaranteed by Minstar for each share of common stock.

AMF also granted Minstar an option to purchase AMF's leisure division for approximately $300 million.

Rocco Portanova, a spokesman for AMF, said he was unable to explain the significance of this provision. He said more details on the offer would be provided on Monday.

AMF leisure division makes bowling, tennis, golf and boating gear. AMF also has an industrial division which makes process equipment for the chemical and oil industries and other machinery.

AMF had a profit of $14.9 million on sales of $1.1 billion in 1984.