U.S. stock index futures rose on Tuesday as lawmakers tentatively agreed to raise the debt limit to avert a default, while shares of Nvidia led an early rally among chipmakers and AI-related firms.

U.S. President Joe Biden and Republican House of Representatives Speaker Kevin McCarthy on Sunday signed off on an agreement to temporarily suspend the debt ceiling and cap some federal spending.

The U.S. House Rules Committee said it will meet at 3:00 p.m. ET (1900 GMT), to discuss the debt ceiling bill.

A handful of Republican lawmakers have said they will oppose it, in a sign that the bipartisan agreement could face a rocky path through Congress.

Reflecting investor optimism, the cost of insuring exposure to a U.S. debt default fell further on Tuesday, while yields on longer-dated U.S. Treasuries fell. [US/]

Nvidia Corp gained 3.2% in premarket trading after it said on Monday it was building Israel's most powerful AI supercomputer to meet soaring customer demand for AI applications.

Shares of heavyweight AI-players including Microsoft Corp and Alphabet Inc rose about 1% each.

Other chipmakers including Advanced Micro Devices Inc, Marvell Technology Inc and Intel Corp added about 3% each.

At 5:00 a.m. ET, Dow e-minis were up 69 points, or 0.21%, S&P 500 e-minis were up 19.5 points, or 0.46%, and Nasdaq 100 e-minis were up 136.75 points, or 0.95%.

(Reporting by Shreyashi Sanyal in Bengaluru; Editing by Shounak Dasgupta)