NEW YORK (CNN/Money) - The union representing production line workers at aircraft maker Boeing Co. said Friday it will hold another rank-and-file vote on the company's latest offer, and on strike authorization, after company officials charged that the previous vote was tainted.

The rank-and-file members of the International Association of Machinists had held a vote Thursday on what the company had termed its best and final offer on a new labor agreement. They also had voted on whether to strike the company starting 12:01 a.m. Monday.

But the union said it would seal those ballots uncounted after the Federal Mediation and Conciliation Service asked the union and management to return to the negotiating table Sept. 4 in Washington D.C.

The IAM had immediately accepted the FMCS's request, and agreed to extend the contract and postpone any strike in the hopes of new talks. But Boeing had balked at the call for new talks and had criticized the call for more talks, saying it had nothing left to negotiate.

Boeing said Friday it would meet with the FMCS officials, but it was not willing to hold talks with the union again on its final offer.

The union had handed out handbills to members and put a posting on its Web site telling members to vote no on the contract offer and in favor of a strike in order to give the union greater leverage at the bargaining table. Jerry Calhoun, the company's chief negotiator, charged that the request for more talks and union handbills had corrupted the voting process.

Union officials announced Friday that due to membership confusion and concern over Thursday's events, it would hold a revote.

"This Union has always prided itself on the democratic process," said a statement from Mark A. Blondin, President of the union district representing the Boeing employees. "I want to assure you that every member will get a chance to revote on whatever offer results from the meetings in Washington D.C. next week."

But company officials said Friday they still want the union to go ahead and count the votes cast Thursday, even if they believe the vote was weighted against the company's contract offer.

"We contend the ballots should be counted from yesterday, no matter if it is tainted," said Boeing spokesman Chuck Cadena. If a revote does occur, it's our hope its conducted in a full and fair environment, free of some of the things that happened Thursday."

Approval of a simple majority of those voting is needed to accept the company's offer. If the offer is rejected, then a two-thirds majority is needed to authorize a strike. The company said it would comply with whatever vote is counted by the union. Cadena would not predict whether or not membership was willing to accept the company's contract offer.

Most of the 25,000 IAM members at Boeing are veterans of at least one if not more strikes at the company, as the union struck the company in 1989 and 1995.