WASHINGTON — Wendy Davis, the Texas state senator who captured the national spotlight with an 11-hour filibuster against restricting abortion rights, turned up in Washington on Monday with the news that she was considering a run for governor.

“I can say with absolute certainty that I will run for one of two offices: either my State Senate seat or the governor,” Ms. Davis said after a luncheon and speech at the National Press Club.

It was Ms. Davis’s second trip to Washington in as many weeks — a period when she has met with staff members at the Democratic Governors Association, raised money at sold-out fund-raisers, turned up at parties around town and huddled with Emily’s List.

The woman who turned pink sneakers into a symbol of resilience is under growing pressure from fellow Democrats to run.