NEW YORK—American International Group Inc.'s financial position remains “relatively stable,” and its property/casualty operations have “shown some improvements,” according to a report released last Tuesday by the Government Accountability Office.

But a stock analyst warned in a separate report that the troubled insurer's publicly traded shares are “grossly overvalued.”

According to a client note by Cliff Gallant, an insurance analyst at Keefe, Bruyette & Woods Inc., AIG still faces significant challenges as it strives to recover from the government bailout of the company in 2008.

In its report, however, the GAO, which is the auditing arm of Congress, said that since it conducted its last report on AIG in September 2009, the New York-based insurer remains in a stable condition. The GAO noted that the outstanding balance of government assistance provided to AIG is $129.1 billion, which is about $8.4 billion more than the balance on Sept. 2, 2009.

And AIG's core insurance operations are showing signs of improvement, the GAO report said.

“For the first time since the second quarter of 2008, additions to AIG life and retirement policyholder contract deposits have exceeded withdrawals. AIG's property/casualty companies also have shown some improvements,” the report said. However, the insurer continues to operate in a market environment where property/casualty rates are declining, the GAO said.

The report noted that AIG is making progress in repaying government debt, but much of that debt has been converted into preferred equity, the GAO report said.

“Consequently, the government's exposure to AIG is increasingly tied to the future health of AIG, its restructuring efforts, and its ongoing performance,” the report said.

Meanwhile, Mr. Gallant of New York-based Keefe Bruyette downgraded his outlook for AIG shares in an investor note last week.

“Under the current ownership and capital structure, we see little long-term value in the common shares, despite the strength of the underlying franchises,” he said.

Mr. Gallant, who now rates the shares as “underperform,” said Keefe Bruyette's $6 target price for AIG shares is “optimistic and somewhat implausible, requiring an exit of government interests which we believe may not be executable. Without a significant and unusual change in the company's financial and ownership structure, we view a runoff scenario as still realistic.”

Mr. Gallant previously had rated the AIG shares as “market perform.”

“Would AIG be in business today without government aid?” Mr. Gallant asked in the note. “Or consider (President and CEO Robert Benmosche's) public admission that selling all of the pieces of AIG would not be enough to fully repay AIG's debts. Doesn't this imply negative real worth, despite a positive book value calculation?”

He said that “one of the few routes viable and therefore most likely” is conversion of the government-owned shares to common shares, a process that he said would be difficult to execute.

“The process would normalize the ownership structure; but even with all forms of government debt gone, AIG's capital structure would remain highly leveraged, likely putting the company under rating agency pressure in our view. Would the company avoid bankruptcy but still essentially have to go into runoff, unable to write new business? The past destruction of real equity value may yet still prove to be too much to overcome, in our view.”

An AIG spokesman had no comment on the assessment.