 "Asian shares hit near five-month high on US deal hopes")
MSCI's broadest index of Asia-Pacific shares outside Japan advanced 0.6% on Tuesday morning to its highest level since May 23. Tokyo's Nikkei share average also gained 0.6%, hitting a two-week peak.
A number of markets in the region, including Singapore, Indonesia, were closed for holidays.
On Wall Street, signals that politicians were heading towards a deal that would avert a possible US default pushed the S&P 500 index up 0.4% to its highest close in nearly one month.
US S&P 500 E-mini futures added 0.2% early on Tuesday, indicating a firmer open if the gains were to be maintained. US Treasury futures slipped 5 ticks.
The US debt ceiling needs to be raised by October 17.
"Risk sentiment remains resilient despite the lack of a clear breakthrough in the US debt ceiling and government shutdown negotiations," analysts at BNP Paribas wrote in a note.
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"The Japanese yen's initial rally has now fully reversed although in the absence of an agreement the near-term risks are for a stronger yen," they added.
The dollar was at 98.61 yen, recovering from a low of 98.05 hit on Monday. It also stabilised at $1.35560 to the euro after slipping 0.1% on Monday.
Against a basket of major currencies, the dollar was up 0.1%.
The fiscal plan under discussion by senators would raise the $16.7 trillion debt ceiling by enough to cover US borrowing needs at least through mid-February, according to a source familiar with the negotiations. It would also fund government operations through the middle of January.
But any deal needs approval in the House of Representatives, where conservative Republicans have insisted any continued funding must include measures to undercut President Barack Obama's healthcare programme -- non-negotiable for Democrats.
JPMorgan analysts said market reaction to the US budget impasse has been muted so far, though it did not believe investors were complacent.
"Our sense is not complacency, but more a belief that a true default, beyond a technical delay in payments lasting several days, is highly unlikely, and a lack of clarity of what such a default would mean for markets beyond a sense that it will be bad," they wrote in a note.
"Market participants appear to be preparing for the event risk of a delayed payment of US Treasury coupons and principals by adding liquidity and avoiding securities maturing around the debt ceiling deadline."
In the commodity markets, gold fell 0.5% to around $1,267 an ounce.
US crude slipped 0.1% to around $102 a barrel, giving up some of Monday's gains as traders bought contracts to cover short positions ahead of a possible deal in Washington.