By Allison Lampert, David Shepardson and Dan Catchpole

SEATTLE (Reuters) -Striking Boeing workers will vote on Monday on an improved contract offer that includes a 38% pay rise over four years, a larger signing bonus and carries the endorsement of their union, which told members it had extracted all it could from the planemaker.

The latest offer, presented on Thursday, comes at a critical moment for Boeing, which this week announced it would raise up to $24.3 billion to shore up its battered finances as a seven-week strike by more than 33,000 U.S. West Coast factory workers worsens its cash burn.

"In every negotiation and strike, there is a point where we have extracted everything that we can in bargaining and by withholding our labor. We are at that point now and risk a regressive or lesser offer in the future," the International Association of Machinists and Aerospace Workers (IAM) said.

Members rejected two earlier offers from Boeing.

The planemaker's shares rose 2.8% in after-hours trading after the offer was announced earlier in an exclusive report by Reuters. Shares had closed down 3.2% on Thursday.

Talks between the two sides were held this week with the assistance of Acting U.S. Secretary of Labor Julie Su. The union vote will come the day before the U.S. presidential poll, which is a dead heat between Democrat Kamala Harris, who would be expected to continue the Biden administration's pro-union policies, and Republican Donald Trump.

An approved deal would be a boost for new Boeing CEO Kelly Ortberg, who is pushing for a "fundamental culture change" at the company after a mid-air door panel blowout in January that put the spotlight on its safety and quality record.

The strike has halted production of its strongest-selling 737 MAX jet and its 767 and 777 widebodies.

Boeing said in a statement it encourages "all of our employees to learn more about the improved offer and vote on Monday, Nov. 4."

An end to the strike would also benefit aerospace suppliers that have been furloughing workers and holding off on new capital investments, as well as airlines facing extended aircraft delivery delays.

APPROVAL NOT GUARANTEED

It is not yet clear how union members will vote. The negotiating team had been pushing for a 40% wage increase and the return of a defined-benefit pension that members lost a decade ago.

Last week, some 64% of workers rejected an offer of a 35% general wage increase over four years that was not endorsed by the union.

Boeing's first offer of a 25% wage increase, which was endorsed by the union, was rejected by nearly 95% of workers in September.