To cheers, smiles and chants of “Vamos United,” Mayor Vincent C. Gray and leaders of the District’s pro soccer franchise inked a tentative deal Thursday that paves the way for the construction of a 20,000-seat stadium in Southwest Washington in as little as three years.

“The winningest franchise in the history of Major League Soccer will be staying right here in the nation’s capital,” Gray (D) said at the Buzzard Point stadium site, standing in front of the team’s managing partner and three businessmen with ownership interests in the underlying land.

But while several key city lawmakers on Thursday endorsed the complex, $300 million public-private stadium plan by the District and D.C. United, significant financial and political hurdles remain.

City officials said they have outlined a deal with only one of the three private landowners — the real estate developer Akridge, which has agreed to trade its two-acre plot plus cash to the city for the site of the Frank D. Reeves Center government building. And news of that transaction generated wary reactions among some of the D.C. Council members who will have to approve key aspects of the deal.

The sale of the Reeves Center “gives me pause,” Chairman Phil Mendelson (D) said. “I don’t understand why it’s in the best interest of the District. . . . It’s an asset, and it’s important that government offices be in places the residents can access them.”

A series of land swaps and agreements will be required for D.C. United to get a new stadium at Buzzard Point.

But in an encouraging sign for stadium backers, Mendelson said the soccer deal was “substantially distinct” from the city’s financing of Nationals Park — a deal that Mendelson strenuously opposed nine years ago.

“There’s value to having professional sports teams based in the District,” he said. “The question is, how much incentive do we need to provide?”

Other council members wasted no time in endorsing the deal, including Marion Barry (D-Ward 8), who said it has his “100 percent support,” citing planned new government offices in Anacostia as part of the deal.

Perhaps no council member’s support is more crucial to the plan’s success. As mayor in the early 1980s, Barry developed the Reeves Center in a bid to revitalize the U Street corridor, and Gray administration officials have worried that his opposition could scotch any deal.

That fear appears, for now, unjustified. “It’s going to be just fantastic,” Barry said. “I’m excited about all of these employees coming to Ward 8.”

Gray said the new city building will remain named the Reeves Center, after a prominent civil rights attorney, and will be near Martin Luther King Jr. Avenue and Good Hope Road SE.

Four other council members — Anita Bonds (D-At Large), Jack Evans (D-Ward 2), David Grosso (I-At Large),and Tommy Wells (D-Ward 6) — attended the news conference and pledged support.

Evans, chairman of the council’s Finance and Revenue Committee and a key architect of the Nationals Park financing, said “this is an easier deal” than the ballpark arrangement, where the city floated more than $600 million in bonds supported by ballpark revenue and a business tax.

“I think you’re going to have a lot of support for this,” he said. “This is not controversial like the baseball stadium was.”

A key council member who did not attend, Economic Development Committee Chairwoman Muriel Bowser (D-Ward 4), offered more measured comments.

“Obviously we love soccer, and we love D.C. United, but I want to hear more about what the deal entails,” she said. “What’s more important is that the residents of the District of Columbia get a good deal.”

The term sheet signed Thursday by Gray and Jason Levien, D.C. United’s managing partner, provides an outline of how the deal will move forward, leaving many details to be hashed out later.

The city agrees to acquire and clear the land for the stadium, costing an estimated $140 million to $150 million, leasing it to the team for $1 a year over the “useful life” of the facility. The team agrees to build the stadium and assume all other costs of the project at a price not set out in the term sheet; the team has said it expects to spend $150 million. Payment of taxes and fees to the city is subject to a complex revenue sharing agreement that would be finalized in a later contract.

The deal sets out an ambitious timeline, starting with the city agreeing to assemble the land no later than Jan. 1 and have the site ready for construction by March 2015. The stadium is required to be “substantially complete and ready for commercial operation” by Jan. 1, 2017. Each of the milestone dates can be changed by the mutual consent of the city and the team.

Gray called the agreement “a very creative plan” that allows the city to finance the land acquisition and infrastructure costs without tapping the city’s limited borrowing capacity. He said he hopes to have legislation enabling the various land swaps, street closings and tax consideration submitted to the council by year’s end.

The term sheet is between the team and the city and, aside from setting a cost target of $100 million, does not address the city’s efforts to secure the land.

In addition to the Reeves Center swap with Akridge, City Administrator Allen Y.Lew would have to secure two other land deals for its agreement with United to stick, and neither is complete. Investor Mark D. Ein and Pepco own significant plots and have yet to reach deals to sell them.

Pepco, the electricity supplier for the District and suburban Maryland, owns about 45 percent of the needed land, where it operates a substation. Thomas H. Graham, Pepco region president, has said he was in “preliminary” discussions about relinquishing the site.

Ein said he was approached recently about a swap for industrial properties he controls along S Street SW. “If there’s a way to do something and it’s fair, then I’m open to it,” he said Thursday.

Neither Ein nor city officials would specify which city properties could be swapped. But Lew mentioned Thursday that the city is seeking to redevelop the Henry J. Daly Building, the police headquarters at 400 Indiana Ave. NW.

Tim Craig, Steven Goff and Jonathan O’Connell contributed to this report.