NEW YORK (CNNMoney.com) - Negotiators from General Motors Corp., bankrupt auto parts maker Delphi and the United Auto Workers union met throughout the weekend and are making progress towards a much anticipated cost saving agreement, according to both company and union officials.

"They've been constructive, but we're not at the point of announcing anything," said Delphi spokesman Lindsey Williams. He said negotiators worked late into the night Sunday and were expected to be back at the negotiating table Monday.

Neither Williams nor GM spokesman Jerry Dubrowski nor union spokesman Paul Krell would comment on some press reports that the three sides were close to an agreement.

"All I would say is the talks are constructive and progress has been made," said Krell. "But I'm not going to speculate on how close an agreement is. In my experience in talks like these, close and near are awfully subjective terms."

But the reports of the three sides being close to a deal helped lift shares of Dow component GM (up $0.31 to $21.44, Research) more than 1 percent in early-afternoon trading early Monday.

The talks are seen as crucial to efforts at both GM and Delphi (Research) to cut the parts supplier's labor costs and become competitive with the non-union North American auto plants operated by Japanese competitors. A failure to reach an agreement with Delphi and the union could prompt a strike at Delphi that could halt production at GM and perhaps even cause a bankruptcy filing there.

GM has contract obligations to its former workers at Delphi, which was spun off from the automaker in 1999. The No. 1 carmaker said in late Thursday it now expects the cost of its obligations related to Delphi to be at least $5.5 billion, or $3.6 billion after taxes, although the cost could reach as high as $12 billion. The low end of the range of its exposure had been $3.6 billion, or $2.3 billion after taxes, before that statement.

In addition, GM has announced its own plans to close 12 plants and facilities and trim 30,000 union-represented jobs in North America.

The Detroit News reported Monday that the three sides have agreed on the offer of early retirement packages to tens of thousands of hourly workers at GM and Delphi as part of turnaround efforts at both companies. The plan is designed to clear positions at GM that would allow Delphi workers to return and trim Delphi's costs.

But the paper reports that the "flowback" of Delphi workers to GM is the main hurdle remaining in the negotiations.

Delphi, which filed for bankruptcy protection Oct. 8, is nation's largest auto parts maker and also the largest supplier of parts to GM. It is demanding sharply lower labor costs and has said it would go to the bankruptcy court and ask that the judge in the case void its labor contract if it does not reach a tentative labor deal by March 31. But Delphi has set and abandoned some earlier deadlines for the same legal move, and officials with GM and the UAW have questioned how firm the March 31 deadline is.

For a look at GM's latest accounting and financial problems, click here.

For more on why the deal at Delphi is crucial for GM, click here.