SEATTLE (AP) -- Representatives from Boeing Co. and the machinists union met with a federal mediator Thursday as the clock ticked on an unusual two-day contract extension after union production workers soundly rejected a contract offer and voted to strike.

Members of the union representing 27,000 aircraft assembly workers at the aerospace giant voted overwhelmingly Wednesday to strike for an unprecedented second time in three years, then learned both sides had agreed to a 48-hour contract extension at the request of Washington Gov. Chris Gregoire and federal mediators.

Boeing spokesman Tim Healy said Thursday that the mediator was trying to help the two sides find middle ground, but he had no information on the progress of the talks.

"The goal at this point is for us to understand the union's critical few issues and evaluate the situation to see if there is a way to move forward," Healy said. "Right now, we're focused on understanding where the union is coming from and reaching an agreement."

Union spokeswoman Connie Kelliher said its representatives would not comment on the talks while they are under way.

The Seattle Times and Seattle Post-Intelligencer reported Thursday that negotiators for Boeing and the machinists union traveled to a hotel in Lake Buena Vista, Fla. The hotel is also the site of the International Association of Machinists' Grand Lodge convention, which runs through Sept. 14.

The machinists union's international president, Tom Buffenbarger, did not immediately return a call from The Associated Press made late Thursday to his room at the hotel.

"We have agreed with the federal mediator to meet in a neutral place with the union and hope to reach an agreement," Healy told The Associated Press late Thursday.

Kelliher, who is in Seattle, said she was unaware union representatives had traveled to Florida. The union leaders have called for a media blackout of the talks, she said.

The contract had been set to expire at 12:01 a.m. Thursday before being extended to the same time Saturday morning.

The last-minute move to avert a potentially bruising strike that could cost more than 27,000 workers weeks of pay was met with frustration from rank-and-file members who had voted 80 percent against the offer and 87 percent to strike if the offer was rejected, far more than the two-thirds required for a walkout.

Under union rules, anything less than two-thirds for a strike meant the offer would have taken effect by default regardless of the vote to reject it.

Chief negotiator Mark Blondin and Tom Wroblewski, president of Machinists District Lodge 751, were repeatedly shouted down at the union hall Wednesday night with catcalls of "Sellout!" and "What was the strike vote for?"

Boeing Vice President of Human Resources Doug Kight repeatedly turned aside questions at a news conference about whether Boeing was relieved to get another chance to avert a strike by offering a sweeter deal.

"Responding to a request from the federal mediators is appropriate for both sides," Kight said. "My job at this point is to listen to the union."

Boeing's "best and final offer," presented Aug. 28 after talks that began May 8, included bonuses totaling at least $5,000 and averaging $6,400, raises averaging 11 percent, pension increases and a 3 percent cost-of-living adjustment -- $34,000 in average pay and benefit gains per employee, according to the company.

The International Association of Machinists and Aerospace Workers represents about 25,000 workers in District 751 in the Seattle area, 1,500 in District 24 in Gresham, Ore., a Portland suburb, and about 750 who do military work for Boeing in Wichita, Kan.

Analysts say a strike could cost Boeing about $100 million per day in deferred revenue. During the last strike -- a 24-day walkout in 2005 that was one of the shortest in company history -- Boeing was unable to deliver more than two dozen airplanes on schedule.