Asian shares rose on Tuesday, diverging from New York markets that slipped on concern about President Donald Trump's ability to focus on economic policies.

Oil prices were mixed amid fears growing US production will offset OPEC cuts.

MSCI's broadest index of Asia-Pacific shares outside Japan rose almost 0.5 per cent, after pulling back slightly in early trade.

Japan's Nikkei fell 0.2 per cent.

Australian shares were up 0.3 per cent. They started soft and moved up on expectations the central bank would hold rates at a policy meeting, which it did.

On Monday, US shares indexes posted losses of as much as 0.37 per cent.

“The reversal in Asian shares was a little bit surprising," said James Woods, global investment analyst at Rivkin in Sydney.

He attributed the changed course partly to views that Trump is now “making progress on his promises", citing progress toward repealing Obamacare.

“The other part is the technical aspect,” Woods said. "Things are looking positive, we're seeing positive data reports, so investors are taking the dips as buying opportunities.”

Republicans had unveiled a legislation to dismantle the Affordable Care Act on Monday, calling for an end to health insurance mandates and rolling back extra healthcare funding for the poor.

Congressional Democrats denounced the Republican plan, saying it would hurt Americans by requiring them to pay more for healthcare, to the benefit of insurers.

Trump's allegations over the weekend that he was wiretapped by his predecessor Barack Obama, without offering any evidence, also raised concerns about his ability to focus on his promised economic measures, including tax cuts and a boost to infrastructure spending.

The euro was fractionally higher at $1.0587, following a 0.4 per cent slide on Monday after former French Prime Minister Alain Juppe ruled out standing in the country's presidential elections.

On Monday, European stocks posted losses, with Deutsche Bank's falling 7.9 per cent, the biggest drag on the FTSEurofirst 300 index after the German lender unveiled an 8 billion euro ($8.47 billion) cash call as part of a major reorganisation.

But declines were limited by merger deals. One involved French carmaker PSA Group and General Motors, and another was between Standard Life and Aberdeen Asset Management

The dollar index, which tracks the greenback against a basket of trade-weighted peers, was steady at 101.60, after Monday's 0.1 per cent gain.

The dollar added almost 0.1 per cent to 113.98, after Monday's 0.15 per cent loss.

The Australian dollar advanced 0.3 per cent to $0.7603.

In commodities, US oil was steady at $53.19 a barrel, following Monday's 0.2 per cent drop, on ongoing concerns that US production growth may undermine output cuts by the Organization of Petroleum Exporting Countries.

Global benchmark Brent retreated 0.1 per cent to $55.96.

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