OLYMPIA, Washington (Reuters) - Machinist union leaders rejected a second contract offer from Boeing Co, which would have secured work on the new 777X jetliner for the Seattle area, because it differed little from an offer that union members had already rejected by a large margin, a key union official said. Leaders of the International Association of Machinists and Aerospace Workers District 751 rejected the offer on Thursday without a membership vote, a decision that has sparked controversy, with Washington Governor Jay Inslee among those weighing in. "We've heard from some rank-and-file members and from leadership of the International that the agreement that emerged deserves a vote," he said in a statement. "That should happen soon, as I have become increasingly concerned that we are at a perilous point in our effort to bring the 777X to Washington state." In a statement emailed to Boeing machinists on Friday and posted on a union website, District 751 President Tom Wroblewski said the company's offer was not sufficiently improved from one union members had voted down by a 2-1 margin last month. The company demanded that the union's top officials voice support for the proposal as a condition of its being put to the members for a vote, Wroblewski said. "When I said we couldn't do that, Boeing withdrew the offer immediately," Wroblewski said. Hundreds of union members emailed their leadership overnight asking why they wouldn't have the opportunity to vote on a proposal the company has labeled its final offer, Wroblewski said. The union's position was thrown into some confusion when Rich Michalski, from the union's national leadership, told the Seattle Times newspaper late Thursday that there was much to like in Boeing's offer and that the rank-and-file should get to vote on the new offer. "I'm sorry that there has been confusion over this issue," Wroblewski said in the email to his members. "I understand that many of you are frustrated, and I don't blame you." A Boeing spokesman said Friday that the company's offer had not been taken off the table but that union officials had turned it down. "Boeing did not withdraw its counterproposal, nor was there any need to do so, because the counterproposal was rejected," Boeing spokesman Doug Alder said by email on Friday. He declined to say if the offer was contingent on the union leadership's endorsement. Talks between Boeing and union officials resumed this week and the sides spent several hours over three days in meetings discussing ideas for an eight-year contract extension stretching to 2024. Union officials made an offer to Boeing on Wednesday, the terms of which were not made public, and Boeing made a counterproposal on Thursday. Boeing's latest offer included an increase in the cash bonus for all machinists to $15,000 from $10,000, dropped plans to reduce the pace of wage increases for new workers and offered concessions on dental benefits, company and union officials said. But it didn't alter the earlier Boeing proposal's cuts to other health care benefits or its conversion of workers' defined-benefit pensions to 401k-style retirement savings accounts going forward. After the union turned down the first contract offer last month, Boeing received proposals from 22 states interested in hosting production of the 777X, the company said on Thursday. (Reporting by Alwyn Scott in New York and Jonathan Kaminsky in Olympia, Wash.; Editing by Eric M. Johnson, John Stonestreet and Peter Galloway)