The New York-based financial company said in a regulatory filing that if the offer is successful it won't file for bankruptcy and will pursue a restructuring through other unspecified ways.
CIT Group, one of the nation's largest lenders to small and midsize businesses, has been scrambling to find new funding as it wrestles with liquidity pressure and maturing debt. The government had refused to save the company last week.
Earlier this week, major bondholders agreed to provide CIT with a $3 billion rescue loan, but it cautioned that the loan might not be enough to head off a cash squeeze.
At the same time it agreed to the loan, CIT launched the cash-offer for $1 billion worth of senior notes due Aug. 17 and warned it may have to file for bankruptcy if it failed.
Under CIT's amended note buyback offer disclosed Friday, holders of certain notes due in August will get an extra $50 per $1,000 principal of the notes if they tender them by July 31 for a total of $825 per $1,000 in principal.
Its shares rose 14 cents, or 19 percent, to 88 cents in premarket trading Friday. Over the past year, its shares have traded as low as 31 cents a share and down from a high of $13.
The Wall Street Journal, meanwhile, reported Friday that CIT had rebuffed as too low an offer from two conglomerates to buy parts of the company earlier this year but was now considering a similar breakup of its own. The newspaper cited unidentified people familiar with the matter.
The newspaper said Warren Buffett's Berkshire Hathaway Inc. and the holding company Leucadia National Corp. made a joint offer in the spring to buy parts of CIT but were rebuffed. It did not say how much was offered nor what the parts were.
The newspaper said CIT and its advisers are in the early stages of evaluating a similar breakup, and said its aviation-finance group and rail finance operations are most likely to be offered for sale.
Should CIT collapse, some experts fear it would deal a crippling blow to an economy still losing hundreds of thousands of jobs a month despite a nearly $800 billion federal stimulus program.
The retail sector would be hit especially hard. CIT serves as short-term financier to about 2,000 vendors that supply merchandise to 300,000 stores, according to the National Retail Federation. Analysts say 60 percent of the apparel industry depends on CIT for financing.
CIT received $2.3 billion from the government's Troubled Asset Relief Program last fall - money that could be lost if CIT files for bankruptcy.
The Federal Reserve put the company through its "stress test" last week and found it faced a $4 billion capital shortfall.