BIRMINGHAM, Ala.. (Reuters) - Alabama's Jefferson County extended talks over a $3.14 billion sewer bond debt in a bid to avert what would be the largest municipal bankruptcy in U.S. history, the county commission president said on Thursday.

The talks were "extremely fragile" and the aim of the extension was to win further concessions from creditors, said commission president David Carrington after an executive meeting at which the county could have filed for Chapter 9.

The county's creditors include JP Morgan Chase & Co.

"We have reviewed the creditors offer in exhaustive detail, point by point. We are working on a counter-offer to their proposal," Carrington told a commission meeting.

After the meeting, finance commissioner Jimmie Stephens said: "There were many good points within their proposal, but we feel it is prudent for us to give some minor adjustments and to give one final and best shot to solving this crisis."

Had the county declared bankruptcy, it would have been the second U.S. municipality this week to take the highly unusual step. The small city of Central Falls, Rhode Island, filed for Chapter 9 on Monday over an $80 million unfunded pension and retiree health benefit liability.

Both places are in part casualties of the U.S. financial crisis as is Vallejo, California, which went bankrupt in 2008. The largest previous Chapter 9 filing was Orange County, California, in 1994.

(Writing by Matthew Bigg; editing by Tom Brown and Andre Grenon)