Marriott's deal increases the amount of cash being offered to Starwood shareholders. Starwood shareholders will own approximately 34% of the combined company's common stock after completion of the merger.
The counterbid - made by Anbang, along with the NY private equity firm J.C. Flowers and Primavera Capital of China, whose chairman, Fred Hu, is the former chairman of Goldman Sachs for China - offered $78 a share in cash last week, worth about $13.2 billion.
"We expect to accelerate the growth of Starwood's brands, leveraging Marriott's worldwide hotel development organization and owner and franchisee relationships".
Starwood has almost 1,300 properties in about 100 countries.
Having Anbang buy Starwood would keep their much-beloved hotel chain independent of Marriott.
They said they expected the deal to close by midyear.
Shares of Starwood Hotels jumped on Monday after it agreed to a sweetened US$13.6 billion deal with Marriott, spurning last week's competing bid from a group led by China's Anbang Insurance Group Co.
Marriott is offering 0.8 of its stock for each Starwood share plus US$21 in cash per share.
This trumps the earlier merger bid made by Marriott of $12.2 billion, which, if it goes through will create the world's largest hotel company.
Should the merger fall through, Starwood would now be required to pay a break-up fee of $450m and $18 of costs connected to the financing of the transaction.
If Anbang's offer had gone through, as Commercial Observer reported on Friday, Starwood would have continued to operate as is, whereas if Marriott were to purchase Starwood, there would be significant layoffs, a source with intimate knowledge of the deal previously said.
"We have a positive view of the increased cash component and Marriott's willingness to lever up to get this deal across the finish line", he said in a report. Marriott and Starwood have each agreed to convene its respective stockholder meeting to consider the transactions contemplated by the amended merger agreement on March 28, 2016 and to immediately adjourn such meeting until April 8, 2016.
Shares of Starwood rose 4.4% premarket to $84.15 while shares of Marriott edged 0.6% lower to $72.75.
To promote the merged brands, the company offered a promotion in 2000 that allowed Hilton HHonors members to earn 2,000 points and 500 miles for every $2,0000 spent at any of its properties.
It is unclear however, whether Anbang and its partners will lodge an improved bid; the company has so far been reluctant to comment on its attempts to acquire Starwood. The company also announced that it has signed a Letter of Intent to convert the famed Hotel Santa Isabel into a member of The Luxury Collection.