TOKYO (Reuters) - Japan's Nikkei share average rose on Monday to its highest level since July 1990, buoyed by optimism over a U.S. debt ceiling deal and a weaker yen.

Shares of Japanese chip-related companies continued to outperform after AI euphoria lifted Wall Street peers.

The Nikkei (.N225) jumped as high as 31,560.43 within the first 10 minutes of trading, although gains mitigated over the course of the session to see the index last up 1.7% at 31,427.38.

U.S. President Joe Biden said on Sunday he had finalized a budget agreement with House Speaker Kevin McCarthy, and the deal was ready to move to Congress for a vote. However, the deal has drawn fire from hardline Republicans and progressive Democrats

"The deal is not done, so there's still a level of risk, but the basic agreement has seen risks recede, and both sides have committed to avoiding a technical default," said Maki Sawada, a strategist at Nomura Securities.

"The Nikkei crossed the psychological 31,500 mark today, but in the end that level proved a bit too heavy," she said. "This week, I expect the Nikkei to steadily advance, but with short-term retracements to check its speed."

The broader Topix (.TOPX) rose as high as 2,175.13, but failed to get close to last week's 33-year high at 2,188.66. It was last up 1.1% at 2,169.66.

The Nikkei's higher weightage towards exporter stocks saw it reap greater gains from the yen's drop to the cusp of 141 per dollar for the first time in six months. A weaker currency buoys the value of overseas revenue.

Honda Motor (7267.T) rallied 2.5% and Nissan (7201.T) rose 1.5%.

The Nikkei's top performer was Advantest (6857.T), the chip-testing equipment maker that counts Nvidia Corp (NVDA.O) among its clients. Shares of Advantest surged up to 6.9% to a record high, and are set to extend a three-day rally, if gains hold.

Of the Nikkei's 225 components, 191 rose, while 31 fell and three were flat.