The bidding was for Conoco Inc. continued yesterday as Seagram Co. offered to buy at least 51 percent of Conoco for $92 a share, up $7 from its most recent offer, and disclosed that millions of Conoco shares had already been tendered to the big Canadian distiller.

The new bid, worth $4.1 billion, sweetens the old offer by more than $300 million and gives Conoco shareholders until Aug. 5 to tender their shares. The old offer was to run out today.

The announcement by Joseph E. Seagram & Sons Inc., Seagram's U.S. subsidiary, came the day after Mobil Corp. said it was "considering" boosting its cash offer for about half of Conoco's shares from $90 to $95 a share. Mobil's aim would be to meet E.I duPont de Nemours & Co.'s $95-a-share cash offer. Mobil did not raise its offer yesterday.

Conoco, whose management is bitterly resisting the Seagram and Mobil offers, issued a statement citing the advantages of DuPont's bid and attacking Seagram's. The statement stressed possible tax advantages in accepting DuPont stock over Seagram cash and pointed out that since Seagram has not bound itself to accept more than 51.5 percent of Conoco shares, other shareholders would be in a minority position.

In another development yesterday, Mobil filed suit in Delaware's Court of Chancery to force Conoco to release its shareholder list. Mobil said that Conoco refused the oil company access to the list Tuesday and Wednesday. A hearing is scheduled for 2 p.m. today.

The new suit intensifies a legal effort that began when Mobil went to court Wednesday to block a portion of Du Pont's friendly takeover deal that would allow Du Pont to buy 15.9 million shares of Conoco treasury stock. For its part, Conoco filed an antitrust suit Wednesday to block Mobil's takeover attempt.