Just when everyone thought Blackstone Group LP, led by Stephen Schwarzman, could get whatever it wanted in the buyout world, along comes Steven Roth of Vornado Realty Trust to spoil his party.

Mr. Roth outbid Mr. Schwarzman on January 17 by offering $37.6 billion for Equity Office Properties Trust, whose collection of office towers is the largest in America and the prize in a takeover battle as landlords vie to dominate coastal cities such as New York, Washington, and Los Angeles where rents are rising the fastest. Billionaire Sam Zell, Equity Office’s chairman, is playing Blackstone against Vornado to extract the highest price.

“We just got topped by a few dollars,” Mr. Schwarzman said at a January 19 conference at the University of Pennsylvania in Philadelphia where he talked about Blackstone’s $36 billion offer for Equity Office.

Blackstone, which has never had a rival scotch a real estate purchase once its proposal was accepted, faces the most significant challenge in 15 years to its real estate ambitions as Mr. Schwarzman seeks another $10 billion from investors. Mr. Roth, who in June said every deal Vornado passed up in the past decade was “a mistake,” is going after properties on the two coasts and his partners would divide up the rest of Equity Office’s 543 office buildings with 103 million square feet.

“You may see Blackstone bring in another partner to strengthen their bid,” a fund manager at New York-based Cohen & Steers Inc., Equity Office’s largest shareholder with about 28.9 million shares and Vornado’s fourth-largest with about 6.76 million shares, Jon Cheigh, said.

Equity Office in November accepted Blackstone’s offer and left the door open to higher bids by saying it would pay a $200 million breakup fee to Blackstone if it does a deal with anyone else. Blackstone has the right to match any rival offer. Equity Office this week opened its books to Vornado and its two real estate partners and said it expects a definitive proposal from Mr. Roth’s group by January 31.

The fight for Chicago-based Equity Office pits Mr. Roth, 65, who built Vornado over 27 years from an owner of discount department stores into Manhattan’s biggest commercial landlord, against Mr. Schwarzman, 59, who has helped lead about $160 billion of leveraged buyouts since he co-founded Blackstone in 1985. Mr. Schwarzman now oversees companies with annual revenue of $85 billion and 380,000 employees.

Blackstone’s real estate group is among the world’s most active, having made 181 transactions with a total value of more than $43 billion, including debt.

Mr. Roth founded Interstate Properties in the 1960s with David Mandelbaum, a New Jersey attorney who still sits on Vornado’s board. Together they invested in Vornado Inc., an appliance maker that owned Two Guys Discount Department Stores, a chain of outlets in New Jersey. By 1980, they gained control of Vornado in a proxy battle, closed the stores and developed strip malls on the sites.

Blackstone’s offer of $48.50 a share in cash, or $20 billion, with assumed debt pushing the price to $36 billion, was backed by Mr. Zell and Equity Office’s board on November 19. Blackstone already sweetened terms to buy out Equity Office bondholders.

Vornado, along with Starwood Capital Global Group LLC, the Greenwich, Connecticut-based firm run by Barry Sternlicht, and Chicago-based Walton Street Capital LLC, have offered $52 a share in cash and stock for Equity Office.

Shares of Vornado rose $2.23 to close at $124.65 in New York Stock Exchange composite trading. Equity Office gained 26 cents to $52.70.