As leaders of the draftsmen’s union at Bath Iron Works met again Tuesday with company officials in an attempt to reach agreement on a new four-year contract, local union officials released a statement warning of a strike and accusing the company of engaging in “unfair labor practice issues.”

Members of the Bath Marine Draftsmen’s Association, Local 3999 of the International Union of United Automobile Workers, voted “overwhelmingly” on Sunday against the company’s “last, best and final offer,” and said they would prepare for a strike should continuing negotiations this week not succeed, according to union officials.

On Monday, the union, which represents about 700 of BIW’s approximately 6,000 employees, issued a statement on its Facebook page announcing that both parties had agreed to a one-week contract extension, with the company agreeing not to engage in a lockout before Sunday and the union agreeing not to strike before that date.

According to the contract extension agreement, signed by union and company officials, the existing collective bargaining agreement was signed Sept. 16, 2013, and expired Sept. 17, 2017. The extension expires at 12:01 a.m. Sunday.

The proposed contract would expire March 20, 2022, according to official documents.

Union officials have contacted a federal mediator and planned to contact senior leadership of the United Automobile Workers and Maine’s congressional delegation, officials wrote.

A key issue is BIW’s proposal to eliminate most of the flexible schedule benefit, which union leaders say has benefitted members, Trent Velella, vice president of the union, said in a release Tuesday.

“Flexibility in the workplace has allowed members to balance the needs of their families including children, aging [parents], and personal medical and health issues while designing some of the world’s finest Navy ships,” UAW Region 9A director Julie Kushner said in the release, adding that the UAW International fully supports the local Bath union.

“There are mechanisms in the existing contract language which allow for the union and the company to work together in order for the flexible work schedule to be effective for all parties,” Velella said. “Over the last several years, the union has experienced four years of wage freezes and the loss of pension benefits for new members. The proposed elimination of this non-economic benefit now, given the recognized positive impact, makes no sense and would only harm morale and productivity.”

The only time the union went out on strike was for three weeks in 1967, according to its website.

Should the local union strike, members would be eligible for a strike benefit of $200 per week plus medical assistance, according to a statement from the UAW.

In December 2015, the largest union at Bath Iron Works — Local S6 of the machinists union — voted to accept a four-year contract that did not include pay raises but did offer annual bonuses.

On Monday, Lisa Read, a spokeswoman for General Dynamics, which owns Bath Iron Works, would only say that the company continues to negotiate with the union. Read said Tuesday that the company had no comment.