By Joshua Schneyer

(Reuters) - Harold Hamm, the chief executive of oil driller Continental Resources who is embroiled in a bitter divorce, offered to pay his former wife $974.8 million, but she rejected a hand-written check, lawyers for both sides said on Tuesday.

Hamm's offer would have paid his ex-wife, Sue Ann Arnall, immediately the full cash value of what he owes based on a November divorce ruling by an Oklahoma County judge.

The lawyers said Arnall did not want to accept the check for fear of hurting her appeal of that decision.

Michael Burrage, Hamm's lawyer, said in an email that Arnall could still cash the check if she wants to, and Hamm had borrowed funds to ensure there would be enough cash in his account to cover it.

Hamm's offer to pay his ex-wife should stop the interest of more than $93,000 per day that has accrued on the award since November, his lawyer said.

One of Arnall's lawyers, Ron Barber, said that she has no plan to cash the check since accepting Hamm's payment could hurt her appeal. Arnall and Hamm both appeared in Oklahoma court on Tuesday, in part seeking to clarify how much of the November award to Sue Ann should be made available to her pending appeals in the case.

Oklahoma County Judge Howard Haralson did not offer a dollar amount. Hamm's lawyers said that Arnall could file an application for temporary relief or borrow money to fund her appeal and living costs if necessary.

Both Arnall, who was formerly Sue Ann Hamm and resumed using her birth name after the divorce, and Hamm have appealed the November divorce judgment. Appeals are set to be heard by the Oklahoma Supreme Court, Reuters reported earlier.

"We are seeking clarification of the court's November 10 order at today's hearing and can not accept any payments, pending such clarification, without jeopardizing Ms Arnall's rights on appeal," Barber said in an email

Arnall, a former Continental executive who was married to Hamm for 26 years, contends that her award of around $1 billion in cash and assets was inadequate and allowed Hamm to keep the lion's share of a fortune her lawyers valued as high as $18 billion.

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Hamm had already paid his former wife more than $20 million during the divorce proceedings.

Hamm's appeal contends that the $1 billion award was too steep. Hamm has lost billions tied to the value of his 68 percent stake in Continental in recent months, which his legal team blames on the sharp fall in oil prices.

ONE OF BIGGEST U.S. DIVORCES

The dueling appeals are the latest twist in one of the largest divorce cases in U.S. history. The contest pits America’s biggest owner of oil against an attorney ex-wife intent on showing that the Hamm fortune stemmed from hard work – both his and hers – during a 26-year marriage.

Hamm contends his Continental stake, which he owned before meeting Arnall, surged in value during the marriage due to “passive” or market factors, like rising oil prices.

Oklahoma law says only marital wealth stemming from active efforts or skills of either spouse should be split in a divorce.

The appeals risk dragging Hamm and his Oklahoma City-based oil company deeper into a divorce battle that is already in its third year. The fight has entailed tens of millions of dollars in costs and a 10-week trial that ended in October.

The case was conducted mostly behind closed doors, after the judge ruled that opening it would harm Continental.

November's judgment, while one of the biggest on record, allowed Hamm to retain his majority stake in Continental, the top driller in North Dakota’s oil boom.

But the value of his Continental shares has fallen by more than half, to around $8.2 billion, since the trial started in August. The company has said its CEO's divorce has not had an impact on its business or operations.

(Additional reporting by Brian Grow in Atlanta.; Editing by Cynthia Osterman)