ANCHORAGE  Two days after he was convicted on seven felony counts in Washington, Senator Ted Stevens returned to Alaska on Wednesday night to begin a six-day campaign sprint, telling several hundred supporters at a rally here that he would be vindicated on appeal and asking them to elect him to a seventh term.

“I will represent Alaska in the senate while my lawyers pursue the appeals to clear my name,” Mr. Stevens said.

Mr. Stevens faces a strong re-election challenge from Mark Begich, the mayor of Anchorage, a Democrat. Even as top Republican leaders have called on Mr. Stevens to resign and many political experts believe his chances of re-election are slim, some people refuse to rule out the possibility of his winning, given his stature here.

Image Senator Ted Stevens autographed campaign signs after his return to Anchorage. Credit... Al Grillo/Associated Press

The senator, a 40-year incumbent known for delivering billions of dollars of federal money and projects to Alaska, was met in an airplane hangar here on Wednesday night with chants of “We need Ted.”