"We continue to negotiate and exchange proposals,"GM told FOX Business on Wednesday.
The union said GM's latest offer failed to meet union members' needs.
"There were many areas that came up short, like healthcare, wages, temporary employees, skilled trades and job security to name a few," Terry Dittes, vice president of UAW's GM Department, wrote in a letter cited by the The Detroit Free Press.
"We have responded today with a counterproposal and are awaiting GM's next proposal to the union," he wrote.
Meanwhile, a parts shortage caused by the strike forced GM to stop production at its pickup truck and transmission factories in Silao, Mexico, on Tuesday morning. Approximately, 6,000 workers were affected, GM told FOX Business.
In negotiations so far, conditions for temporary workers have been a sticking point for the UAW. Temps are union members doing the same work as permanent employees, but earning half the pay and far fewer benefits.
The union wants those workers to get a path to permanent positions as well as compensation closer to that of their permanent counterparts.
GM counters that employing temporary workers is good for permanent employees because they enable the full-time staff to take time off. Hiring temps also gives the company flexibility to scale up production for new models and handle absenteeism.
The Associated Press contributed to this report.