OCEANPORT, N.J. (AP) _ The purse for the 1987 Haskell Invitational, which is shaping up as rematch between Bet Twice and Alysheba, has been raised to $500,000, Monmouth Park General Manager Hal Handel announced Friday.

A meeting between Alysheba and Bet Twice would be their first since Bet Twice denied Alysheba a sweep of the Triple Crown by winning the Belmont Stakes.

''The interest in the Haskell has been quite intense,'' Handel said. ''Director of Racing Bobby Kulina expects to invite most of the best 3- year-olds in training.''

The 1 1/8 -mile Haskell originally was to have a $300,000 purse. The Grade I stakes is scheduled to be run Aug. 1.

Both Alysheba, who won the Kentucky Derby and the Preakness, and Bet Twice currently are stabled at Monmouth Park.