Stock markets gained ground on Tuesday while investors mulled the level of US electoral uncertainty after President Donald Trump returned to the White House following treatment for COVID-19.

As Trump was discharged from hospital, political concerns persisted ahead of the presidential election on November 3.

Tokyo stocks opened higher, extending Wall Street rallies.

The benchmark Nikkei 225 index was up 0.44 per cent or 103.36 points at 23,415.50 in early trade, while the broader Topix index advanced 0.43 per cent or 6.99 points to 1,644.24.

Japanese shares are supported by a "receding sense of uncertainty with the news of President Trump's discharge from hospital, and expectations for additional US economic stimulus", Mizuho Securities said in a commentary.

As for oil prices, they shot higher amid strikes on Norwegian offshore platforms and a hurricane heading towards US installations.

In afternoon exchanges, the FTSE 100 index was 0.2 per cent higher in London, while the Dow Jones index had gained the same in early New York trades.

Global equities had rebounded on Monday on reports of Trump's improving health, and as US lawmakers appeared to edge towards agreeing on a new stimulus package.

The election was still a big question mark, however.

"This is still going to be a controversial, drawn-out election with the potential added uncertainty of a challenge to the result," according to OANDA analyst Craig Erlam.

Investors were also unclear over the chances of a new US stimulus package that would help counteract fallout from the pandemic in the world's biggest economy, dealers said.

Analysts said Trump's positive test for COVID-19 could be the jolt US lawmakers needed to finally agree a deal.

Stimulus talks have revived with a series of mostly phone meetings between Treasury Secretary Steven Mnuchin and Democrat House leader Nancy Pelosi.

"As far as traders are concerned, talking is preferable to being in a stand-off and not engaging with each other", noted David Madden, analyst at CMC Markets UK.