U.S. stock futures were in the green and 10-year Treasury yields fell back below 5% in early European trade, as lower oil prices soothed sentiment after the Federal Reserve's rate hike Wednesday.

Brent crude oil fell below $104 a barrel following media reports of better-than-expected recovery in Gulf infrastructure. Saudi Arabia is aiming to restore half the capacity of its East-West pipeline within days, according to a source cited in a Bloomberg report.

Lower oil helped pull Treasury yields lower. Yields on 10-year Treasurys fell below 4.980% after closing above 5% for the first time since 2007 in the last session. Two-year and 30-year yields also pulled back from highs.

Stocks benefited from lower oil prices. The Dow Jones Industrial average is currently enduring its worst start to September since 2008, losing 3.2% so far this month. Futures for the index pointed to a limited recovery, jumping 0.8%. Futures for the S&P 500 gained 0.85%, while Nasdaq futures rose 1% as technology stocks across both hardware and software gained.

Stocks had sold off while yields jumped following the Fed's rate decision Wednesday, with Federal Reserve Chair Kevin Warsh warning that inflation remains "too high and has been for too long." His comments raised the prospect of further rate hikes to come.

However, the chair's hawkish tone reassured some investors that the Fed will act to bring down inflation, amid uncertainty around Warsh's ability to withstand political pressure.

"We are now becoming more confident that Warsh's Jackson Hole speech and yesterday's action marked important steps toward reestablishing policy credibility," said Marco Valli, chief economist at UniCredit.

Equities were also positive in Europe, with banks and technology stocks rallying. The continent-wide Stoxx 600 gained 0.6%. The picture was less rosy in Asia, where stocks broadly fell following the selloff in U.S. hours. Hong Kong's Hang Seng index lost 0.6%, though Japan's Nikkei 225 added 0.3%.

The dollar weakened slightly but remained elevated after hitting a seven-week high following the Fed rate hike. The Japanese yen depreciated following the hike, despite a widely expected rate increase from the Bank of Japan Friday. Bitcoin strengthened modestly, holding above the $76,000 mark, while gold weakened slightly to trade below $4,371.20 a troy ounce.

For the day ahead, macro attention switches to the Bank of England's policy decision. The central bank is expected to hold rates, though sticky inflation is driving expectations for a November hike.