By Timothy Gardner

Aug 31 (Reuters) - The Illinois legislature is edging closer to a vote as soon as Tuesday on a bill that aims to prevent two nuclear power plants from shutting, as the owner moves to close one next month unless the state acts.

The legislature could vote in a special session on a new version of a wide-ranging energy bill introduced Monday that allows nuclear plants to earn carbon mitigation credits for generating virtually emissions-free power. The session is on legislative mapping, but could include the energy bill vote.

"Talks continue in efforts to reach agreement," said John Patterson, a spokesperson for Don Harmon, a Democrat and the Illinois Senate president.

Exelon Corp has said it will close the Byron nuclear plant in mid September and the Dresden plant in November if a state or federal program does not come to the rescue.

Gina McCarthy, President Joe Biden's climate adviser, has said existing nuclear plants are "absolutely essential" to hit U.S. goals to decarbonize the electric grid by 2035 and the administration has supported federal incentives for nuclear.

Incentives are included in bipartisan infrastructure and reconciliation bills being considered by the U.S Congress. But Exelon has said these alone would come too late to save Byron and Dresden.

While many Illinois lawmakers and Governor J.B. Pritzker, a Democrat, back legislation to save the nuclear plants, the bill has been delayed on disagreements on issues including when coal and natural gas plants would be phased out or be required to add emissions-capturing technology. The Byron and Dresden plants have more than 1,500 workers, many in high-paying union jobs.

"Hopefully ... we can finish up what little is left on the table," Illinois State Senator Sue Rezin said at an Illinois Senate hearing late on Tuesday. A Republican, she has the Dresden plant in her district.

Exelon did not immediately respond to a request for comment.

The United States has 93 nuclear reactors, more than any other country but down from 104 in 2012 as aging plants struggle to compete with power generated by solar and wind farms and plants that burn natural gas. (Reporting by Timothy Gardner; Editing by David Gregorio)