By Tim Gaynor and David Schwartz

PHOENIX (Reuters) - With several hundred thousand ballots still to be counted in the race for an Arizona Senate seat, a Democrat who earlier conceded the race to his Republican rival was gaining and appeared to have a distant shot at the seat after all.

Former U.S. Surgeon General Richard Carmona conceded on election night last Tuesday to six-term U.S. Congressman Jeff Flake after about three quarters of precincts had reported, showing Flake with a lead of about six percentage points.

But nearly a week later, with more than 340,000 ballots yet to be counted, the tally has tightened to about four points, leaving the Carmona campaign watching closely to ensure that each and every ballot is counted.

The most recent results show Flake in the lead by 79,547 votes in a race in which 2 million ballots were cast.

"We're monitoring it closely, and we want every ballot to get counted, and we will take any necessary steps to make sure that happens," said Carmona campaign spokesman Andy Barr.

It is very unlikely the outstanding ballots could overturn the result of the race in Arizona, which has not returned a Democratic Senator since Dennis DeConcini won office in 1988.

But Barr said the campaign, which is now down about 4 percentage points, expected to gain ground as the tally continues over coming days.

"The count is going very, very slowly, and it is hard for us to know where it will end up," he told Reuters.

As of Monday afternoon, the Secretary of State's office reported that an estimated 171,889 early votes and 171,047 provisional ballots had yet to be tallied statewide.

The Democrat's candidacy was boosted in part by a drive to register throngs of Hispanics riled by the state's two-year-old crackdown on illegal immigration. Such a large uncounted vote has prompted an outcry from some Hispanic and civil rights activists about the fairness of the voting process. Continued...