A day after the union representing Pepco workers overwhelmingly rejected what the company called its final contract offer, Pepco and union officials have agreed to meet Friday to continue contract negotiations.

The union, International Brotherhood of Electrical Workers Local 1900, rejected Pepco’s “last, best and final” offer by about 5 to 1, union president James A. Griffin said Wednesday night. On Thursday, Griffin said Pepco and the union are likely to schedule additional meetings next week.

Griffin added that the union is working on a counterproposal that it will be ready to show Pepco officials next week. He declined to discuss any details about the new proposal.

In a text message, Pepco spokeswoman Myra Oppel confirmed the Friday meeting.

“We hope that we can reach an agreement,” Oppel said. “We are absolutely willing to continue negotiating.”

The union and Pepco have been at an impasse for months over contract negotiations and worries of a possible strike — the first in 27 years — are looming. This would come at a bad time for the utility, which has been castigated for service shortfalls and outages after last summer’s derecho storm.

Pepco’s contract proposal included annual wage increases over four years— 2.25 percent the first year and then 2.5 percent annually, Pepco said. Workers have received annual wage increases of 2 percent or more since 1999, Pepco said.

The union wasn’t asking for larger raises. Instead, it raised objections to several provisions in the company’s new offer.

Griffin said his largest concern was that Pepco wants to eliminate the union’s ability to arbitrate changes to its health and welfare plans in favor of a different, more arduous process. In response, Pepco officials said the contract would limit the changes the company could make.