General Motors assembly workers picket outside the General Motors Bowling Green plant during the United Auto Workers national strike in Bowling Green, Kentucky, October 10, 2019.

The United Auto Workers union said on Friday that it had countered General Motors' latest offer and "if GM accepts and agrees to this group of proposals, we will have a tentative agreement."

In a letter to union members, UAW Vice President Terry Dittes, who oversees the union's GM department, said that negotiations will continue over the weekend to reach a tentative agreement.

"Brothers and Sisters, your support and perseverance has provided this entire bargaining team the energy to keep pushing and fighting for you, your families, your communities and all the working men and women in this country," Dittes said.

General Motors urged UAW Thursday to agree to "around-the-clock" bargaining in an attempt to reach a tentative agreement and potentially end the union's strike against the automaker, which is now in its 26th day.

In a Thursday letter obtained by CNBC, GM Vice President of North America - Labor Relations Scott Sandefur criticized the union for not promptly responding to a Monday offer from the company. He also encouraged the union to "engage in bargaining over all issues around-the-clock to get an agreement."

"Your members and our employees' lives are being disrupted, and they deserve our commitment to getting any remaining issues resolved as quickly as possible," Sandefur wrote to Dittes.

Sandefur, in the letter, said the company has repeatedly urged the UAW to participate in "around-the-clock" bargaining. Since the strike began Sept. 16, negotiations have been ongoing but have mainly ended in the early-evening.

Sandefur's letter follows another message obtained by CNBC from Dittes to Sandefur that discussed a Wednesday meeting between the union and company that included UAW President Gary Jones and GM CEO and Chairman Mary Barra, among others.

Barra, according to two people familiar with the negotiations, has been "involved" in the talks. One source said she has allowed Sandefur and others to lead the day-to-day negotiations. The Wednesday meeting is the first Barra has attended with the union leaders.

As part of its revised offer, GM boosted the amount it plans to invest in the United States to about $9 billion from its previous offer of $7 billion, a source familiar with the offer said.

Of the new total, $7.7 billion would be invested directly in GM plants, with the rest going to joint ventures including a potential battery plant near the Lordstown, Ohio, factory that has been idled, the source said.

GM stock closed up 2.6% at $35.57 on Friday.

The company said the offer also includes increased compensation through wages and one-time payments, preserving industry-leading healthcare benefits without increasing workers' costs, enhanced profit sharing with unlimited upside and a higher ratification bonus than the $8,000 previously offered.

For temporary workers, GM said its offer would create a path to permanent employment and include a ratification bonus.

Read the full letter from Terry Dittes to union members on Friday below: