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 13 cents, or 17 percent, to 87 cents in midday 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.
Buffett told the Fox Business Network on Friday that CIT has a competitive disadvantage because it is paying too much interest on the money it borrows.
"You can't pay loan shark rates and compete with people who are getting their money on a government guaranteed basis for practically nothing," Buffett said on Fox.