Val Kilmer is continuing politicking as he considers running for governor, this time with a visit to Washington, D.C. that includes attending a speech on American Indian issues and paying visits to the offices of at least three members of the New Mexico congressional delegation.

Kilmer was in attendance at Tuesday’s speech in Washington by Joe Garcia, of the Ohkay Owingeh pueblo in northern New Mexico, to the National Congress of American Indians. Garcia heads the organization.

There Kilmer ran into U.S. Sen. Tom Udall, according to Udall spokeswoman Marissa Padilla.

Following the speech, Kilmer stopped by Udall’s office yesterday and again today, Padilla confirmed. He didn’t have an appointment, but he talked briefly with some of the staffers in Udall’s office and, today, was able to spend some time talking with Udall about Garcia’s speech, Padilla said.

Kilmer also stopped by U.S. Rep. Ben Ray Luján’s office today, Mark Nicastre, Luján’s communications director, confirmed. The congressman was in a hearing and missed Kilmer’s visit. Nicastre said he understands that Kilmer “was visiting a few congressional offices today.”

Kilmer will be meeting with Sen. Jeff Bingaman on Thursday, Bingaman spokeswoman Jude McCartin confirmed.

A spokesman for Rep. Martin Heinrich has not provided comment on whether Kilmer has visited his office. Sara Schreiber, communications director for Rep. Harry Teague, said Kilmer has not stopped by Teague’s office or met with anyone from the office.

Teague is a close friend of Lt. Gov. Diane Denish, and Schreiber is Denish’s daughter. Kilmer, a registered Democrat, would face Denish in a primary if he runs for governor. She’s been actively campaigning for the job since 2007. (I should also point out that a Teague staffer took the Kilmer photo I use as a mug shot in this posting.)

Kilmer, who is openly considering running for the state’s top job in 2010, has been visibly politicking in the last few weeks. Last week he made two appearances at the Roundhouse in Santa Fe (click here and here for the stories) and granted an interview to an Associated Press reporter — his first formal interview with a New Mexico journalist about his political ambitions. In January, he attended President Barack Obama’s inauguration. In December, he attended his first UNM Lobo basketball game.