Bob Benmosche will continue as chief executive of bailed-out insurer American International Group Inc., having made sufficient progress in his treatment for cancer, the company said Monday.

AIG said last October that Benmosche was receiving aggressive chemotherapy for an undisclosed cancer but that he intended to remain CEO into 2012, health permitting. Benmosche said in a statement his doctors believed he could continue working for 12 to 18 months.

Benmosche’s health has been a looming question as the company and government prepare for a massive share sale this year.

AIG and the U.S. Treasury are expected to sell at least $15 billion in stock in May, and Benmosche recently told Reuters he intended to participate in the pre-deal roadshows to pitch the shares to investors.

In case something changes, though, AIG said its existing succession plan will remain in place. Chairman Steve Miller would step in as interim CEO if needed until the company  named a permanent replacement.

The news is likely to cheer AIG employees, some of whom have been known to break into tears at the mere mention of Benmosche’s illness.

“While none of us knows precisely how much time we have in life, I now know that I have the luxury of more time than I might have imagined. I am going to make the most of it,” Benmosche said in a letter to AIG employees announcing his plan to stay.

AIG shares ticked slightly higher in after-hours trading, to $42.10 from a $41.95 close. At those levels, the U.S. Treasury stands to make a profit of nearly $27 billion on its 92 percent stake in the company.