Activity was thin, however, with many markets closed or trading for a half-day only before the Christmas holiday.
By 0956 GMT, Britain's FTSE 100 was down 0.6 percent, while France's CAC and Spain's IBEX had eased 0.9 and 0.6 percent respectively. Germany's DAX and Italy's FTSE MIB were shut.
"Markets still under pressure from last week's more hawkish Fed update, exacerbating fears about slowing growth and more expensive refinancing following years of stimulus," said Mike van Dulken, Head of Research at Accendo Markets.
European shares are down nearly 14 percent year-to-date and on track for their worst year since 2008, having fallen back to a two-year-low on last week's rate outlook from the U.S. Federal Reserve.
The UK's complicated divorce from the EU, Italy's contested budget and a trade spat between Washington and Beijing have also been weighing this year, forcing analysts to progressively cut their earnings growth estimates for European companies.
On Monday, investors were also fretting about political stability in the United States after an aide to President Donald Trump said the partial government shutdown could continue into the new year.
Corporate news was thin but the pan-European exchange operator Euronext said it aimed to buy the Oslo stock exchange for 625 million euros. Euronext shares fell as much as 0.7 percent before recovering most of its losses.
Advertising companies WPP and Publicis were among the biggest losers, down 2.3 and 2.6 percent.
S4 Capital, the marketing venture set up by former WPP boss Martin Sorrell, was flat on its first trading day on the London Stock Exchange's main market.
The British restaurant and hotel owner Whitbread rose 0.9 percent after receiving clearance from the European Union for the sale of its Costa coffee chain to Coca-Cola.
The clearance paves the way for a 500 million pound share buyback.
Among major European benchmarks, Germany's export-oriented DAX index, which is heavily exposed to China, is set to be the worst performer, down more than 17 percent so far in 2018.
France's CAC is down 12.5 percent, the FTSE 100 down 13.1 percent and Italy's FTSE MIB down 15.8 percent.