A softening labour market and a cooling economy have traders perking up with expectations of a September rate cut from the Federal Reserve, lifting stocks and keeping the dollar under pressure.

There are still worries though that the economy could miss a soft landing and head for recession - that battle between "bad news is good news" and "bad news is bad news" is keeping investors on edge.

European stock markets are set for a higher open, futures indicate, with the continent-wide STOXX 600 hoping to shrug off Tuesday's drop ahead of PMI data from the euro zone, France and Germany.

The European Central Bank's policy meeting on Thursday will likely keep risk appetite in check as traders await comments to get clarity on how the central bank will follow up after a widely expected rate cut this week.

Asian stocks were broadly higher after data showed U.S. job openings fell more than expected in April to the lowest level in more than three years, leading the markets to price in a 65% chance of a rate cut in September and 45 basis points of easing this year.

The data drove Treasury yields lower and weighed on the dollar, which was hovering near a two-month low against a basket of six rivals.

The focus shifts to nonfarm payrolls data on Friday.

In Asia, the spotlight remained on Indian markets after Tuesday's spectacular drop after election results showed a victory margin for Prime Minister Narendra Modi that fell short of expectations.

India's Nifty 50 index was volatile in early trading, hinting at investor worries over the prospect of a coalition government that may not be as market friendly as previously hoped.

Meanwhile, a report on Monday that online broker E*Trade may consider banning Keith Gill, the meme-stock influencer who ignited frenzied trading in shares of GameStop in 2021, has triggered a backlash on social media sites.

E*Trade-parent Morgan Stanley declined to comment on the report and the messages on social media calling for a boycott of the brokerage platform.

Key developments that could influence markets on Wednesday:

Economic events: Composite and services PMI data for May from France, Germany and euro zone; S&P services and composite PMI May data for UK.

(Editing by Sam Holmes)