The rallies followed another record finish on Wall Street overnight, where investors shrugged off worries about a US criminal probe of the Federal Reserve central bank.

Tokyo's Nikkei index surged as much as 3.6 percent in early trade, driven by anticipation that Prime Minister Sanae Takaichi will capitalise on strong poll numbers by calling an election.

Takaichi became Japan's first woman prime minister in October and her cabinet has an approval rating of around 70 percent.

But her ruling bloc only has a slim majority in parliament's powerful lower house, hindering her ambitious policy agenda.

It would be "significant to have the foundation of the Takaichi administration solidified" in national polls, brokerage house Monex said.

"If a lower house election is confirmed, we can anticipate a renewed buying trend."

Hong Kong shares were up 1.5 percent and Shanghai gained 0.2 percent, while Seoul and Singapore both rose 0.5 percent.

Taipei was up 0.6 percent, and Sydney jumped 0.9 percent.

It came after New York's Dow and S&P 500 ended at records for a second straight day.

The tech-rich Nasdaq index also bounced back from early losses after Sunday night's disclosure of the US Department of Justice probe into the Federal Reserve.

Broad optimism over the global economy and technological advances such as artificial intelligence have buoyed market sentiment in recent months.

Oil prices rose on Tuesday after US President Donald Trump on Monday announced a 25 percent tariff on any country trading with Iran, ramping up pressure on Tehran over its violent crackdown on a wave of protests.

Michael Wan at MUFG noted that Iran makes up three percent of global oil production, with Venezuela supplying around one percent "as a rough rule of thumb".

"China stands out as the top trading partner for Iran, both across exports and imports, and also in terms of its position as the top importer of Iranian crude oil," he said.

Trump said in a social media post on Monday that the new levies would "immediately" hit the Islamic republic's trading partners who also do business with the United States.

"This Order is final and conclusive," he wrote, without specifying who they will affect.

Chinese electric vehicle giant BYD, which last year overtook Elon Musk's Tesla to become the world's largest EV maker, jumped 4.5 percent in Hong Kong, along with other Chinese companies in the sector.

The European Union had on Monday offered China an alternative to tariffs in a bitter trade dispute over the bloc's hefty duties on Chinese-made electric cars.

- Key figures at around 0200 GMT -

Hong Kong - Hang Seng Index: UP 1.5 percent at 27,014.90

Shanghai - Composite: UP 0.2 percent at 4,171.18

Tokyo - Nikkei 225: UP 3.2 percent at 53,576.08

West Texas Intermediate: UP 0.4 percent at $59.73 per barrel

Brent North Sea Crude: UP 0.4 percent at $64.10 per barrel

Euro/dollar: DOWN at $1.1659 from $1.1666 on Monday

Pound/dollar: UP at $1.3470 from $1.3466

Dollar/yen: UP at 158.48 yen from 158.17 yen

Euro/pound: DOWN at 86.55 pence from 86.63 pence

London - FTSE 100: UP 0.2 percent at 10,140.70 (close)

New York - Dow: UP 0.2 percent at 49,590.20 (close)