China's Anbang Insurance Group has raised its offer for Starwood Hotels & Resorts Worldwide to almost $14 billion.
The increased bid is the latest challenge to the US hotel operator's merger with Marriott International.
The bidding war for Starwood has pitted Marriott's ambitions to create the world's largest lodging company with about 5,700 hotels against Anbang's drive to create a vast portfolio of US property assets.
The acquisition of Starwood, owner of the Sheraton and Westin brands, by Anbang would be the largest ever by a Chinese company in the US.
Anbang's consortium, which includes private equity firms JC Flowers & Co and Primavera Capital Ltd, has offered $82.75 per share in cash, in what is reasonably likely to lead to a proposal that is superior to the deal with Marriott, Starwood said.
Marriott's latest cash-and-stock offer, which was announced on March 21, is currently worth around $78 per share.
Starwood's board has not yet changed its recommendation to its shareholders in support of the company's merger with Marriott, Starwood said.
A vote for Starwood shareholders to approve the Marriott deal is scheduled for April 8.
Marriott declined to say if it would raise its offer further.
In a statement, it said it was confident that the previously announced amended merger agreement with Starwood is the best course for both companies.
"Starwood stockholders should give serious consideration to the question of whether the Anbang-led consortium will be able to close the proposed transaction, with a particular focus on the certainty of the consortium's financing and the timing of any required regulatory approvals," Marriott said in its statement.
Marriott said last week it believes it could achieve $250m in annual cost synergies within two years after closing the deal with Starwood, up from $200m estimated in November 2015 when it signed its original merger agreement.
An acquisition of Starwood by Anbang would probably face scrutiny by the Committee on Foreign Investment in the US, an interagency panel that reviews deals to ensure they do not harm national security.
However, sources have said both Starwood and Anbang believe that deal would receive CFIUS clearance.