By Alwyn Scott SEATTLE (Reuters) - Boeing Co said on Tuesday it is narrowing its list of sites for building its newest jetliner, the 777X, to "a handful," signaling its determination to consider locations outside Washington state where it now builds similar planes. In a letter to employees, Boeing Commercial Airplanes Chief executive Ray Conner said the company received proposals for 54 sites from 22 states, and aimed to cut the list down to a few top picks this week. Boeing opened the competition to all-comers after machinist workers in Washington, who currently build 777 planes, rejected a contract offer. Conner did not say whether Washington state would be on the short list, and Boeing declined further comment. Conner's remarks appeared to harden the standoff that began when union leaders rejected a contract offer last week that would have eliminated pensions and said Boeing had withdrawn the offer. The union, the International Association of Machinists District 751, said Boeing wanted its leaders to unanimously endorse the new contract offer and sell it on the shop floor. "Our guys said, 'No, we can't do that,'" District spokesman Bryan Corliss said on Tuesday. Corliss said Boeing withdrew the offer after union leaders declined to endorse it. Conner acknowledged asking union leaders to support the offer and put it to a vote. But he said they rejected it "plain and simple, and we now have to turn and face the reality of the union leadership's final decision." The location of the new jet is a key concern. Boeing's 777X will be a derivative of its top-selling wide-body plane, with new wings and engines, due out in 2020. Along with Boeing's narrow-body 737 MAX jet due in 2017, it is expected to be Boeing's only new jetliner program for the next 15 years. If it goes to another state, it could mark the beginning of a long winding down of aerospace work in Washington state. Many analysts say Washington offers the lowest risk and costs because Boeing already builds the 777 there, giving it ready access to a trained work force and state incentives that include low-cost land, easy permitting and $8.7 billion in tax incentives passed by lawmakers last month. Because of the high stakes for the state's major industry, IAM District 751 President Tom Wroblewski is under pressure from elected leaders to put the second offer to a vote. A group of union members plan a rally on Wednesday near the Everett, Washington, plant where the current 777 is built to show support for a vote on the latest offer. With just under 31,000 members, however, the rally would need to draw a sizeable crowd to show the IAM that members really want to consider the deal. (Reporting by Alwyn Scott; editing by Andrew Hay)