General Motors Co. will shut down a car assembly plant in South Korea by the end of May as part of a restructuring effort amid tepid demand for its vehicles, the U.S. automaker's local unit said.

The factory to be closed in the western port city of Gunsan has been increasingly underutilized, operating at roughly 20 percent of capacity over the past three years, according to a statement Monday by GM Korea Co.

The local arm said it has proposed to its labor union and the South Korean government a concrete plan to remain in the country and turn the loss-making business around, which it said would require the full support of all parties.

The proposal includes significant investment in South Korea that would preserve thousands of jobs, it said.

"As we are at a critical juncture of needing to make product allocation decisions, the ongoing discussions must demonstrate significant progress by the end of February, when GM will make important decisions on next steps," Barry Engle, GM executive vice president and president of GM International, said in the statement.