Trump hosts Jensen Huang at White House as Nvidia tops $4 trillion market cap

• Nvidia CEO Jensen Huang met with President Donald Trump at the White House on Thursday, CNBC's Megan Cassella reported.
• The meeting comes as Nvidia rose slightly on Thursday, becoming the first company to close a trading day with a market cap over $4 trillion.
• Nvidia has been grappling with export controls on its AI chips implemented by the Trump administration in April for national security reasons.

Nvidia CEO Jensen Huang met with President Donald Trump at the White House on Thursday, CNBC's Megan Cassella reported.

The meeting comes as Nvidia rose slightly on Thursday, becoming the first company to close a trading day with a market cap over $4 trillion, beating Apple and Microsoft to the symbolic milestone. Nvidia touched the mark briefly on Wednesday during trading.

Trump praised Nvidia stock in a social media post Thursday morning.

“NVIDIA IS UP 47% SINCE TRUMP TARIFFS. USA is taking in Hundreds of Billions of Dollars in Tariffs,” Trump posted on Truth Social. “COUNTRY IS NOW 'BACK.'”

An Nvidia representative declined to comment, and it was unclear what the meeting is about, but Nvidia has been grappling with export controls on its artificial intelligence chips implemented by the Trump administration in April for national security reasons.

At the time, the U.S. government told Nvidia that its previously-approved H20 processor — intended exclusively for the Chinese market — would require an export license. Huang previously told investors that requirement effectively cut off Nvidia's sales to China with “no grace period.” The AI chipmaker said that it would miss $8 billion in planned orders for the chip in the company's July quarter.

“The $50 billion China market is effectively closed to U.S. industry,” Huang told investors on an earnings call in May.

Nvidia also faces another potential restriction on AI chip exports after the Trump administration cancelled a planned rule by former President Joe Biden called the “AI diffusion rule.” The Trump administration promised newer, simpler restrictions later this year on which countries could receive Nvidia's technology.