The U.S. dollar and yields on U.S. government debt were under pressure as investors wagered policy tightening in the U.S. would be glacial at best.

The dollar index fell to as low as 95.25 in overnight trade, a level not seen since June 30, when it hit a nine-month low of 95.22. It was last at 95.50 in early trade.

The greenback weakened for the third day in a row against the Japanese yen, touching an overnight low of 112.87, before bouncing back to the 113.00-level.

Meanwhile, yields of the benchmark 10-year U.S. Treasury fell to around 2.31%, the lowest level in a week and well-off highs near 2.39% touched earlier this month.

Yields on the rate-sensitive 2-year Treasury fell to a three-week low of 1.347%, while the yield on the 30-year Treasury bond was also lower at 2.868%.

World shares hit their fourth all-time high in less than a month after dovish comments from Fed Chair Janet Yellen encouraged investors to take on risky positions.

On Wall Street, the blue-chip Dow futures pointed to a gain of 21 points, or around 0.1%, at the open, the S&P 500 futures ticked up 5 points, or about 0.2%, while the tech-heavy Nasdaq 100 futures tacked on 21 points, or roughly 0.4%.

In Europe, stocks were broadly higher, building on the prior day’s sizable jump.

Earlier, Asian shares ended mostly in positive territory, with South Korea's Kospi index closing at an all-time high. India also scored an all-time top, while shares in Hong Kong touched their strongest level in two years.

Investors looked ahead to more comments from Federal Reserve Chair Janet Yellen, who will testify for a second day on the central bank's monetary policy, this time in front of the Senate Banking Committee at 14:00 GMT.

Yellen sounded cautious on inflation and noted the Fed would not need to raise rates "all that much further" to reach current low estimates of the neutral funds rate in her first day of congressional testimony on Wednesday.

She also said that the U.S. economy is healthy enough for the Fed to begin winding down its massive $4.5 trillion balance sheet at some point this year. The speech was seen as mainly dovish by market participants.

Besides Yellen, Thursday's calendar also features PPI inflation data and weekly jobless claims, both due at 12:30 GMT. Investors were already looking ahead to Friday’s U.S. inflation figures for June for their potential impact on Fed policy.

China posted stronger-than-expected June trade figures, bolstered by firm global demand for Chinese goods and robust appetite for construction materials at home.

Exports from the world's second largest economy rose 11.3% from a year earlier, while imports expanded 17.2%, both beating analysts' expectations, official data showed.

That left the country with a trade surplus of $42.77 billion for the month, the General Administration of Customs said.

The data revealed that China's trade surplus with the U.S. was $25.4 billion in June, up from $22.0 billion in May, official data showed, and its widest since October 2015.

An increase in trade between China and nuclear-armed North Korea in the first half of the year could also add to diplomatic pressures between Beijing and Washington.

Elsewhere, OPEC's compliance with production cuts fell in June to its lowest levels in six months as several members pumped much more oil than allowed by their supply deal, the International Energy Agency said in its monthly market report.