Under the terms of a two-year lease extension to continue playing at RFK Stadium, D.C. United will limit seating to the lower bowl and mezzanine level and attempt to sell sponsorships on tarps covering the upper-deck seating areas.

“It’s a great branding opportunity, but it’s more important that our supporters become accustomed to a 20,000-seat stadium, and we expect that limiting the capacity will encourage an increase in season ticket sales,” United President Kevin Payne said Thursday.

United and Events DC, which operates the stadium, are also seeking to sell naming rights to the playing surface.

The new capacity for MLS matches is 19,647 in a facility that is able to accommodate about 45,000 – far too large for United’s purposes. The club averaged 15,196 last year and drew 16,314 for last Saturday’s season opener. The upper deck is rarely utilized. In past seasons, United stuck visiting supporters there, but last weekend, Kansas City fans were in a corner of the lower bowl.

The only turnout last year that exceeded the new capacity was for David Beckham’s visit with the Los Angeles Galaxy (26,622). The Galaxy will not play in Washington this year.

United is one of the few MLS teams that still plays in a large stadium. The others are the Seattle Sounders, who play at CenturyLink Field, home to the NFL’s Seattle Seahawks; and the New England Revolution, who share Gillette Stadium with the New England Patriots.

In Seattle, the upper levels are covered for Sounders games, which attract 36,000 spectators. Most sections are closed for Revolution games, which averaged 13,222 last season.

By limiting seating capacity at RFK, United hopes to create demand and encourage fans to secure seats in advance. It also seems to be an effort to prepare fans for the club eventually playing in a new stadium with seating for about 20,000. United is eyeing a project at Buzzard Point in Southwest D.C., four blocks from Nationals Park.

Most MLS clubs play in stadiums that hold between 18,000 and 27,000 spectators.

In announcing the new lease, Events DC said it would improve lighting on the concourse and renovate restrooms in a facility that opened in 1961. The improvements are part of a “multi-million dollar” plan to upgrade RFK and the adjacent D.C. Armory.

As previously reported by The Post, a facilities fee ($2.25) is being applied to tickets purchased for United matches. Revenue will go toward those capital improvements.

Financial terms of the new lease were not disclosed, but United officials said during negotiations they were optimistic about reaching a more favorable deal.

“We appreciate the spirit of our relationship with Events DC, which is reflected in this new agreement and the improved economics,” Payne said. “We now look forward to engaging in more detailed discussions with the District about a long-term stadium solution for D.C. United.”

Mayor Vincent C. Gray said: “I’m delighted that D.C. United has finalized their lease and will continue to play at RFK. We are hopeful that the team remains in the District and look forward to United bringing home another MLS Cup.”