In 1.54pm trading in New York, the Dow Jones Industrial Average added 0.7 per cent, while the Nasdaq Composite Index climbed 0.9 per cent. In 1.38pm trading, the Standard & Poor's 500 Index gained 0.6 per cent.
Gains in shares of Microsoft and those of IBM, recently up 1.8 per cent and 1.7 per cent respectively, led the Dow higher.
In Europe, the Stoxx 600 Index finished the session with a gain of less than 0.1 per cent. The UK's FTSE 100 Index slipped 0.2 per cent, as did France's CAC 40 Index, while Germany's DAX Index fell 0.3 per cent.
As Deutsche Bank shares traded near a record low amid concerns about a US$14 billion claim from the US Justice Department to settle an investigation into mortgage-backed securities, investors found fresh reasons for concern about the euro-zone's banking industry.
Commerzbank shares dropped after a report it plans to cut jobs and suspend dividend payments, while Credit Suisse Group shares declined chief executive officer Tidjane Thiam warned the bank faced ongoing challenges in the third quarter and is eyeing more cost cuts.
"Markets are nervous, but panic levels haven't been triggered yet," Guillermo Hernandez Sampere, head of trading at MPPM EK in Eppstein, Germany, told Bloomberg. "Some European financials are really not in a very healthy shape, and the market is aware of it. We had a summer during which volatility stayed at the beach, but now we are back in the game and we have to learn to deal with it.
You have the perspective that Trump lost the debate and good consumer confidence numbers.
Oil prices fell along with expectations that OPEC members will reach an agreement on curbing output. Iran said it remains keen to further lift output.
"The gap (in views) between OPEC countries is narrowing. I don't expect that an agreement will come out of the consultations tomorrow," Saudi Energy Minister Khalid al-Falih told reporters, Reuters reported.