TAIPEI (Reuters) - Taipei-listed shares in TSMC hit a record high on Friday after the chipmaker posted forecast-beating third-quarter earnings and predicted a rosy outlook on strong artificial intelligence (AI) demand.

Shares jumped 6% shortly after opening to reach T$1,100 ($34.25), surpassing the previous record of T$1,080 hit on July 11. That gave TSMC a market capitalisation of around $884 billion, the most of any company listed in Asia.

The company, however, appeared to face some political uncertainty after U.S. media outlet The Information said the U.S. Department of Commerce is probing whether TSMC has been making AI or smartphone chips for China's Huawei, whose access to non-Chinese chips has been severely curtailed due to U.S. export controls.

As the world's largest contract chipmaker, TSMC, whose customers include Apple ( AAPL ) and Nvidia ( NVDA ), has benefited from a surge towards AI across a spectrum of industries.

On its earnings call on Thursday, Taiwan Semiconductor Manufacturing Co (TSMC) reported a forecast-beating 54% jump in quarterly profit, raised its revenue forecast for the year and said the next five years would also be "healthy" for the firm.

Venson Tsai, an analyst at Cathay Futures Consultant in Taipei, said the stock could go higher still.

"TSMC's share price hasn't fully reflected the rising wave of AI long term," he said.

Following the media report about the U.S. probe, TSMC said in a statement on Friday that it was a law abiding company and committed to complying with laws and regulations, including export controls.

"If we have any reason to believe there are potential issues, we will take prompt action to ensure compliance, including conducting investigations and proactively communicating with relevant parties including customers and regulatory authorities as necessary," it said.

The U.S. Commerce Department declined to comment.

($1 = 32.1190 Taiwan dollars)

(Reporting by Ben Blanchard; Additional reporting by Karen Freifeld in Washington; Editing by Muralikumar Anantharaman)