Seatac, Wash. ? Hundreds of Boeing machinists and union supporters rallied Sunday outside the hotel where contract negotiations are going down to the wire.

When negotiations resumed afterward at 3:30 p.m. PDT, Boeing raised its offer of a third-year wage increase to 3 percent from 2.5 percent, said machinists union spokeswoman Connie Kelliher.

Tom Buffenbarger, president of the International Machinists Assn., gives a speech to members of the Boeing machinists union during a rally Sunday in Seatac, Wash.

“They just aren’t listening,” Kelliher said, noting top issues of the 25,000-member machinists union are job security, pensions and health care.

Some hard bargaining remains before Boeing makes its final contract offer Tuesday.

Then, on Thursday, union members are to choose whether to accept it. If not, a two-thirds majority would be needed to approve a strike.

With picket signs and chants, supporters gathered Sunday at the site where talks have been going on since Aug. 15.

“This membership has been hammered by layoffs,” said Matt Bates, a machinists spokesman at the rally. “The mood is grim.”

Picket signs were plentiful: “My Dad deserves a good contract,” “Where is my future?” and “Jobs for us.”

Stan Hoit carried a picket sign and a lot of bitterness.

“People feel really betrayed, really dejected,” said Hoit, a tool-and-die maker who’s spent 27 years with Boeing. “It’s all about profits, short term. They’ve completely sold out to the stockholders.”

For its part, Boeing knows its customers are watching very closely, said Chuck Cadena, Boeing spokesman. They want to know they have a reliable partner and that the company is going to make rational decisions to provide affordable products and services, he said.

In the middle is Jeff Clark, a federal mediator called in to help narrow the differences.

“Both sides are working hard to put this together,” Clark said, “but there are certainly a lot of difficult issues that have to get resolved.”

The company’s initial offer included a 6 percent ratification bonus, 2.5 percent pay raises in the second and third years of the contract and a small boost in its pension contribution. But those at the rally weren’t talking about pay, but about longer-term worries.

“Job security is a big key, and we’re getting nowhere on that,” Bates said.

In talks Sunday, Boeing proposed keeping the job-security language in the current contract, which includes a statement that no machinist would lose a job as a direct result of subcontracting or sending jobs overseas.

Boeing has laid off nearly 30,000 workers since Sept. 11 last year. And it’s shifting some of its manufacturing overseas, making union members even more uneasy.

Boeing “cannot artificially guarantee employment,” Cadena said. “Ultimately it’s our customers who determine our job security.”

As for health insurance, the company’s proposal was not well received. Union officials equated the proposal for more contributions by employees to a cut in pay.

Boeing’s Cadena defended the proposal Sunday, saying the plan would have the Machinists pay the same share of health insurance costs as other Boeing employees.

The two sides are far apart on increases in pension payments. Boeing offered a 12 percent increase; the machinists want a 140 percent increase.

The current contract expires Sept. 1 for the union members, who work in Washington, Wichita, Kan., and Portland, Ore. Most of them build commercial jets for the Chicago-based aircraft and aerospace firm.