The offer is the second attempt by the firm to shed jobs in the US since 2006, when General Motors offered voluntary contract buyouts to its 113,000 workers, of which 30,000 accepted the deal.
The loss reflects a slump in its North American market, which has been hit by the US's slowing economy.
'Positive improvement'
For the fourth financial quarter the company posted a net loss of $722 million, or $1.28 per share, compared with net income of $950 million, or $1.68 per share, the previous year.
General Motors also posted combined losses of almost $1.7 billion in North America and Europe that wiped out gains of $437 million from operations in emerging markets in Asia and Latin America.
The company's revenue has fallen despite an increase of three per cent in the number of cars sold.
Rick Wagoner, chairman of GM, said the weak US economy and high commodity prices had hurt turnaround efforts in North America.
He added that a decision to reduce low-profit sales to daily rental companies by 110,000 in 2007 also affected US sales.
"We're pleased with the positive improvement trend in our automotive results, especially given the challenging conditions in important markets like the US and Germany," he said in a statement.
"[However] we have more work to do to achieve acceptable profitability and positive cash flow."
In September last year more than 73,000 GM workers went on strike over healthcare costs, returning to work after a deal was struck between the company and the United Auto Workers union.