Hamm, a legendary oilman who once called the Organization of the Petroleum Exporting Countries a "toothless tiger", is offering $74.28 per share for stock not owned directly or indirectly by him and the Hamm family. The latest offer is 6.1% higher than the original proposal of $70 that Hamm made in June.
The all-cash offer represents a premium of 8.9% to Continental's closing price on Friday and 15% to the closing price when the Hamm announced the initial offer.
Continental's shares jumped 8% in premarket trading on Monday.
The deal would be the most significant in the U.S. shale sector since the surge in oil and gas prices this year after sanctions on major energy producer Russia hit an already-tight supply.
Hamm and the rest of his family already own 83% of Continental's common stock.
(Reporting by Ruhi Soni and Arunima Kumar in Bengaluru; Editing by Maju Samuel and Sriraj Kalluvila)
