A rough day of talks between the school bus drivers’ union and Durham School Services ended with a pledge from the union not to strike today.

Both sides were continuing negotiations Tuesday evening, and the president of the local bus drivers’ union promised a strike would not be called today, even if they hadn’t made a deal by the night’s end.

School buses in Charleston and Dorchester 2 will run their regular morning and afternoon routes.

L.D. Fletcher, president of Teamsters Local 509, said Durham walked out of their scheduled talks Tuesday, but Durham said that wasn’t true.

Fletcher spent most of the afternoon visiting district leaders in Beaufort, Charleston and Dorchester 2, and school officials from Charleston and Dorchester 2 said he assured them the union had no immediate intention to strike.

Durham released a statement earlier in the day saying it remained committed to reaching an agreement that benefits everyone. The company, which employs bus drivers in Charleston and Dorchester 2, said it increased its offer to drivers but still can’t meet the “unreasonable demands of the union.”

“While the union rejected our offer of mediation made earlier in negotiations, we stand ready to continue discussions, whether through continued negotiations or mediation, should they decide to adjust their demands,” said Carina Noble, spokeswoman for Durham, in a statement.

Although a strike wasn’t planned for today, Charleston School Superintendent Nancy McGinley continued to urge parents to have alternative plans in case a strike does happen.

“I have been assured that both sides want to sincerely come to an agreement and will exhaust every avenue to avoid a work stoppage, including consideration for mediation,” McGinley said.

The union has been trying to work out a new employment contract with the company since last July, and contract talks have heated up during the last two weeks. The biggest issue has been bus drivers’ pay.

The union had promised not to strike while talks are ongoing.