Demonstrating its determination to stay in the fight, Mobil Corp. yesterday boosted to $6.5 billion its offer to buy Marathon Oil, thus bettering the deal offered shareholders by U.S. Steel. At the same time, Mobil denounced the agreement between Marathon and the steel producer as a "sweetheart deal."

In a carefully constructed offer, for which Mobil set the stage the day before by winning a court order blocking U.S. Steel's takeover bid, the giant oil company offered $126 a share for at least 51 percent of Marathon's stock and an exchange of Mobil notes for additional Marathon stock. The total value of the bid is approximately $6.5 billion, or an average of about $108 a share for the 60 million shares outstanding.

U.S. Steel last week topped Mobil's original offer with a proposal to pay $125 a share for 51 percent of the stock and to exchange notes for more shares. That package was valued at approximately $6.25 billion, or $104 a share. Mobil's first offer for the reserve-rich, smaller firm would have paid $85 a share for some stock and exchanged notes for other stock in a package worth $5.1 billion.

Neither Marathon nor U.S. Steel had any comment on the new Mobil bid.

Mobil's new offer was carefully conditioned on two options granted U.S. Steel by Marathon being declared null and void. Those options give the steel company the right to buy 10 million shares of Marathon and to acquire a major piece of the company's oil and gas reserves even if a third party such as Mobil wins control of Marathon. The reserves have made Marathon a takeover target.

If those options are upheld, the Mobil offer of yesterday may disappear in smoke. As part of the deal offered yesterday, Mobil retained the right to withdraw it entirely or to buy as little as a third of Marathon's shares. Buying less than 50 percent of Marathon's shares would keep U.S. Steel's hands off the Texas oilfield reserves, blocking U.S. Steel from exercising that option, Mobil noted.

The decision on whether the options are legal and another key decision on whether the Mobil offer violates antitrust laws are pending in two different federal courts in Ohio. Their decisions are expected within the next four or five days.

The outcome of "the plethora of legal uncertainties" that grew out of the increasingly complicated takeover war are key factors, said Sanford Margoshes, an analyst for Bache Halsey Stuart Shields Inc. "For the moment, Mobil has reestablished itself as pre-eminent, but the question is whether that pre-eminence for the moment is enough to outweigh the uncertainties facing the bid," he said.

Just as resolution of the question of the legality of the options will determine where Mobil goes with its takeover assault, a federal court ruling that there are no antitrust obstacles to the Mobil bid would be expected to encourage still more oil companies to jump in. Two potential contenders most often mentioned are Gulf Oil Corp. and Texaco.

At an average price of $108 a share, Marathon is still a good buy, according to analysts. Mobil has said in court that it believes the company's stock is worth approximately $180 a share.

Mobil's new offer provides that the 24.8 million shares of Marathon already tendered to Mobil and not withdrawn will receive the full $126 price. Additional stocks tendered by midnight Dec. 4 will be entitled to be purchased on a pro rata basis if more stock is tendered than Mobil decides it wants to buy. The offer expires Dec. 11.

U.S. Steel's offer required stock to be tendered by Nov. 28 for investors to be sure at least some of their stock will be bought. A federal judge in Columbus extended that date to Dec. 8 earlier this week.

Still another key antitrust decision on the proposed Mobil-Marathon merger is pending before the Federal Trade Commission. Mobil issued a statement yesterday, saying it had delivered to the FTC documents requested under the Hart-Scott-Rodino antitrust act.

Mobil said its understanding is that the 10-day waiting period in which the FTC has to act expires Dec. 5. The documents delivered yesterday filled 147 large cartons and included about 323,400 pages, Mobil said. The company said it had previously delivered another 71 cartons filled with some 160,800 pages of information. Mobil called the FTC request for documents "unusually broadsweeping."

In the meantime, Marathon's stock declined 3/4 to 105 3/4 on the New York Stock Exchange. Mobil was off 5/8 to 25 7/8, and U.S. Steel closed down 1/2 at 29 1/2 in heavy trading.