MSCI's broadest index of Asia-Pacific shares outside Japan were down 0.1 percent in early trade but stood near its eight-month peak hit on Wednesday. Japan's Nikkei was flat.
U.S. stocks ticked up on Wednesday, just enough for the S&P 500 and Dow industrials to set record highs, with investors expecting upbeat earnings to keep the rally going.
Wall Street shares have quickly recovered the losses triggered by Britain's vote on June 23 to leave the European Union, driven by upbeat U.S. economic data.
"Brexit doesn't mean a breakdown of the global financial system after all, nor a major slowdown in the economies outside the UK. Investor activity is slowing down after June 24 but uncertainty is gradually easing," said Koichi Yoshikawa, executive director of finance at Standard Chartered Bank in Tokyo.
In addition, concerns that Brexit could disrupt the European economies effectively took a Federal Reserve rate hike off the agenda in the near future, and boosted expectations of more monetary stimulus from central banks in Europe and Japan.
Financial markets expect the Bank of England to announce a rate cut later on Thursday. Governor Mark Carney has hinted he may ease policy to cushion the economy from the Brexit shock.
The British pound slipped 0.3 percent to $1.3115 in early Thursday trade after having risen to this week's high of $1.3340 on Wednesday as attention shifted towards the Bank of England and away from the political picture in Britain.
Prime Minister Theresa May quickly named leading Brexit supporters to key positions in her new government, including former London mayor Boris Johnson as foreign secretary.
The euro was stuck in its familiar range and last stood at $1.1099.
While the European Central Bank is expected to keep policy on hold at its meeting next week, the euro's overnight index swaps are pricing in further rate cuts over coming months. .
The yen bounced back from two days of big falls earlier this week to trade at 104.10 to the dollar.
Japanese Prime Minister Shinzo Abe called for fiscal stimulus, expected to reach about two percent of GDP, following his election victory on Sunday.
Oil prices bounced back slightly after tumbling more than 4 percent on Wednesday, erasing most of the previous session's gain, as a run of bearish U.S. inventory data heightened concerns about a global glut.
Global benchmark Brent crude futures rose 0.8 percent to $46.41 per barrel in early Asian trade.