On Saturday morning, Sarah Huckabee Sanders, the White House press secretary, said in a statement that President Trump was monitoring the situation. “Federal authorities are assisting with the ongoing investigation, which is being led by local authorities,” the statement said. “We commend the interagency response effort for their swift action and protection of public safety.”

Gov. Jay Inslee of Washington State tweeted late Friday that there were still “a lot of unknowns” about the tragedy. But he thanked the Air National Guard from Washington and Oregon for quickly sending the jets.

“The responding fighter pilots flew alongside the aircraft and were ready to do whatever was needed to protect us, but in the end the man flying the stolen plane crashed,” Mr. Inslee said.

Air traffic controllers communicated with the pilot to try to help him land safely, the Federal Aviation Administration said in a statement.

The Seattle airport was brought to a standstill for part of Friday evening. On one Alaska Airlines flight from Portland, Ore., passengers were stuck on the tarmac after landing and informed by the pilot that there had been an issue with another plane at the airport, and that gates were backed up with 40 planes waiting.

According to the Port of Seattle, which operates the airport, Sea-Tac hosts more than 30 airlines with nonstop service to more than 90 domestic destinations, and almost 30 cities abroad. The F.A.A. ranked it the ninth-busiest airport in the United States for passenger traffic in 2017.

Observers chronicled the plane’s course on social media and listened in to radio traffic in real time. While the plane was still aloft, the man flying it chatted with officials in a frenzied stream of consciousness, commenting on the beauty of the Olympic Mountains, the prospect of jail time and shock at his rapidly fading gas tank.