The NFL’s free agency signing period Tuesday officially reached the one-week mark, and despite meeting needs at several key positions, the Washington Redskins have yet to come to an agreement with leading tackler and team captain, inside linebacker London Fletcher.

Fletcher is coming off of a season that saw him record an NFL-best 166 tackles, which marks a career high, along with two interceptions and 1.5 sacks.

A 14-year veteran, Fletcher will turn 37 in May. But despite his age, Coach Mike Shanahan, General Manager Bruce Allen and defensive coordinator Jim Haslett at various points this offseason have identified re-signing Fletcher as an important move.

“He is a priority for us,” Shanahan said soon after the season ended. “We’d love to have him back, and hopefully he’ll be back and part of our organization for years to come.”

And Fletcher — who has spent the last five seasons in Washington, leading the team in tackles each year — has said he wants to return to the Redskins.

Allen said March 10 he had been in talks with Fletcher’s agent and expressed hope that the linebacker would remain with the team. But for now, the sides remain at odds on a figure that works for both player and team.

It’s unclear how far apart the sides stand, or what type of payday Fletcher seeks. But the linebacker has told people he has a specific figure in mind. It’s believed that it exceeded what Washington was prepared to offer, and that so far, neither has been willing to move.

Fletcher last season earned a base salary of $4.9 million, but the two-time Pro Bowl player could be seeking a payday similar to the one the Baltimore gave Ray Lewis in 2009, which paid him $6.4 million a year with $2.4 million guaranteed.

The inside linebacker market has featured little buzz thus far, with only Dan Connor signing with Dallas (two years, $6.5 million) and Joe Mays re-signing with Denver (three years, $12 million). Then on Tuesday, Detroit re-signed Stephen Tulloch to a five-year deal believed to be in the neighborhood of the $42.5 million Cleveland gave D’Qwell Jackson in February. Meantime, Seattle’s David Hawthorne, Atlanta’s Curtis Lofton and Minnesota’s E.J. Henderson remain on the market.

Tulloch’s signing could help trigger things for Fletcher and the Redskins, who could be waiting to get a better feel both of the free agent market and their other roster needs before deciding how much they are willing to fork over to Fletcher.

The team last week learned that the league has leveled a salary cap hit of $36 million over the next two seasons in retaliation for the way contracts were structured in the uncapped 2010 offseason. That took $18 million of roughly $30 million in cap space Washington planned to use this offseason. But the Redskins still have $9.7 million in cap money to work with, which seems like enough to get a deal done with Fletcher and still be able to meet other needs.

If the Redskins fail to sign Fletcher, they would face the tall task of replacing not only their emotional leader, but also the most productive player on a unit that last season improved from 31st in total defense to 13th in the NFL. Whether the team sought a replacement through free agency or the draft, the new player would have to learn the system and become as comfortable with the play-calling as Fletcher was.

“It’d be a huge loss if we don’t re-sign him,” second-year outside linebacker Ryan Kerrigan said. “I know ‘coach on the field’ gets thrown around a lot, but London really is an extension of Haslett. He knows the calls and everything just as well, and really does a great job of positioning us to make plays. He makes everyone’s job easier.”

Re-signing Fletcher isn’t the only other area in which Washington has struggled in during this free agency signing period. The team has thus far been unsuccessful in attempts to add a right tackle and a left guard. The Redskins also hoped to add cornerback Aaron Ross, but he agreed to terms with the Jacksonville Jaguars late Monday, meaning Washington — which also missed out on Cortland Finnegan, who signed with St. Louis last week — must continue its search for help in the secondary.