Safeco CEO Mike McGavick talked about the company's future at yesterday's annual meeting but did not address his own, which is rumored to...

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Safeco CEO Mike McGavick talked about the company’s future at yesterday’s annual meeting but did not address his own, which is rumored to include a possible run for the U.S. Senate in 2006.

Asked after the meeting whether he intends to seek the Republican nomination, McGavick didn’t rule it out.

“I’m very flattered that people have suggested I could make a contribution like that,” he said.

McGavick, who served as chief of staff to former U.S. Sen. Slade Gorton, R-Wash., said he has met with people about the possibility. But, he said, “at the end of every such meeting, I remind them that I have my hands full, I love it and that’s where things stand.”

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McGavick has led the turnaround of Seattle-based insurer Safeco, which last year saw profits rise by 66 percent despite pretax catastrophe losses of $275.6 million, caused mostly by hurricanes in Florida and nearby states.

Competition is strong, though, and in January led the company to lower its outlook for premium growth to the mid- to high single digits, down from last fall’s forecast of a double-digit increase.

Safeco executives are telling employees to “keep their wits about them” in such a competitive environment, McGavick told shareholders yesterday.

When competition heats up, insurers sometimes push premiums too low in trying to bring in new business.

“There are going to be people making pricing mistakes, and we do not want to be one of them,” McGavick said.

The company announced yesterday that it has raised its quarterly dividend from 22 cents to 25 cents. The next dividend is payable July 25 to shareholders of record as of July 8.

Safeco shares rose yesterday by $1.19, or 2.3 percent, to $53.23.

Melissa Allison: 206-464-3312 or mallison@seattletimes.com