In currency markets, Britain's sterlingGBP= dropped to a six-month low and was last 0.4% lower against the dollar at $1.2462 amid a worsening economic outlook and rising fears about a no-deal exit for Britain from the European Union.
"The Fed's consideration of rate cuts is not only about growth but also about inflation, which remains well below target, and inflation expectations, which were breaking to the downside before the Fed signaled the likelihood of cuts".
Japan's benchmark Nikkei 225 edged down almost 0.2% in morning trading to 21,529.38.
In China, the Shanghai Composite was 0.2% lower and the blue-chip CSI300 was off 0.3%, while Hong Kong's Hang Seng fell 0.7%.
The broader S&P 500 dropped 0.3 per cent to 2,967.08 while the tech-heavy Nasdaq slipped 0.1 per cent to 8,087.11.
Apple's suppliers in Japan, such as Murata Manufacturing and Taiyo Yuden, fell 2% and 4%. Constellation Brands declined 1.7% and Franklin Resources lost 1.2%.
Money market futures are still fully pricing in a 25 basis point (bps) cut at the Fed's next policy meeting on July 30-31, but have nearly priced out a larger 50 bps move.
"We still think the odds favor of a 25 bps "insurance" cut", said Kevin Cummins, a senior United States economist at NatWest Markets.
Global equities will likely remain under pressure after last month's outperformance, Pictet Wealth Management said in a memo on Tuesday. "We expect (emerging market) equities to perform sideways in the coming weeks, but with the possibility of rotation to quality cyclicals".
Federal Reserve Chair Jerome Powell testifies before the US Congress on Wednesday and Thursday and investors have a lot riding on him sounding suitably dovish.
"Whether the negotiators can find a solution to the hard structural issues that remain between the two sides is another matter, and Kudlow cautioned there was "no timeline" to reach an agreement", National Australia Bank strategist Rodrigo Catril said. "There's been some over-dovishness in what the Fed needs to do in the market".
In currency markets, the Turkish lira was down 2 percent against the dollar after Turkey's Central Bank's Murat Cetinkaya was replaced by his deputy Murat Uysal.
In late US trading, the index that tracks the greenback against six other major currencies .DXY was up 0.09% at 97.471 after touching 97.588, which was the highest since June 19. The Russell 2000 index of smaller company stocks added 1.20 points, or 0.1%, to 1,562.59.
Bullion futures settled little changed in New York Monday just days after the metal surged near the highest since 2013 on bets the Fed will lower borrowing costs either at the end of this month or later.
Brent crude oil, the worldwide standard, rose 60 cents to close at $64.76 a barrel. U.S. West Texas Intermediate (WTI) crude futures shed 0.4% to $57.46.
Wilder rematch set for February, says Fury
Tyson Fury has confirmed that he will fight Deontay Wilder in their eagerly-anticipated heavyweight rematch on February 22, 2020. Undefeated Brit Tyson Fury is one of the most famous and highly regarded active boxers in the the current era of the sport.