Asian stocks lost early gains on Tuesday as relief that a possible default by the US government had been averted gave way to concern that the deal to suspend its debt ceiling was a compromise that would have negative consequences.

The package still has to be approved by the Republican-controlled House of Representatives and Democratic-controlled Senate before the debt limit is reached, likely by next Monday.

"The US had a poor resolution to the debt ceiling negotiations with still a huge increase in government debt and no real cuts to spending, but (it) has relieved pressure for now," said James Rosenberg, an advisor at broker Ord Minnett in Sydney.

"There's still a huge disconnect between bond markets and equities. The bond market is implying there is an extreme 70 per cent probability on a US recession in the next year. These signals stand in stark contrast to the resilient equity market."

MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.02 per cent on Tuesday, after US stocks were closed on Monday for the Memorial Day holiday. The index is down 1.3 per cent so far this month.

Australian shares were down 0.11 per cent, while the Nikkei stock index rose 0.36 per cent, after the Japanese benchmark hit a 33-year high on optimism over the US debt deal and a weaker yen, which helps the country's exporters.

Hong Kong's Hang Seng Index climbed 0.31 per cent at the open, but tumbled to be down 0.82 per cent later in the session, extending its recent slide to a new low this year. China's CSI300 Index was down 1.16 per cent.

The Hang Seng lost 7.2 per cent during May, while the CSI300 is off 5.5 per cent as a result of China's economy not recovering from its pandemic closures ending in January as fast as expected.

"Everyone is looking at the disappointment in the performance of China equities recently and that is now creating negative investor sentiment," said Jack Siu, Credit Suisse's greater China chief investment officer.

"Investors are now more muted towards the reopening story of China and are contemplating their positions."

In Asian trade, longer-dated US Treasuries rallied on Tuesday as bond traders welcomed the deal to suspend Washington's borrowing limit until January 2025 in exchange for caps on spending and cuts in government programmes.

Despite an initial positive response, investors say markets are not out of the woods yet. Narrow margins in the House of Representatives and Senate mean moderates from both sides will have to support the bill for it to pass.

Benchmark 10-year yields dropped 6 basis points during Asian trade to 3.7616 per cent, while 30-year yields fell 6.3 bps to 3.9134 per cent.

With the debt deal heading to Congress for approval, JB Were analysts said there could be up to $600 billion worth of bill issuance in the next six to eight weeks.

The size of the Treasury issuance and the economic implications are now being considered, according to Invesco's Asia Pacific global strategist David Chao.

"The recent regional banking crisis in the US, coupled with the Treasury issuances are likely to tighten liquidity conditions," Chao said.

"The announcement of a debt deal in the near term is a boost to market sentiment but it places pressure on growth due to the government spending cuts, the tighter liquidity conditions, but the flipside is the pressure on growth is doing the job for the Fed as it tries to cool the economy. It could place a dampening effect on inflation."

The pan-region Euro Stoxx 50 futures were up 0.14 per cent , German DAX futures gained 0.09 per cent, while FTSE futures were down 0.08 per cent at 7,631

US stock futures, the S&P 500 e-minis, were up 0.23 per cent at 4,223.

The dollar dropped 0.03 per cent on Tuesday against the yen to 140.4 , just below the year's high of 140.91 hit on Monday.

The euro was up 0.1 per cent flat at $1.0702, having lost 2.89 per cent in a month, while the dollar index, which tracks the greenback against a basket of currencies of other major trading partners, slipped to 104.41, just off a more than two-month high. It was also trading near a six-month peak against the Chinese yuan.

US crude dipped 0.7 per cent after to $72.17 a barrel, after earlier trading up by 0.3 per cent. Brent crude fell to $76.42 per barrel.

Gold was slightly lower with the spot price at $1,935.72 per ounce.