The pan-continental Stoxx Europe 600 fell 0.1% in opening trade.
European shares edged lower following a strong session in Asia on Monday, after US stocks surged in the previous session on fresh signs of economic strength and the Federal Reserve said it would be flexible with its interest-rate policy. S&P 500 futures were 0.4% higher.
Nomura chief China economist Ting Lu said Beijing's latest moves to unlock liquidity in the financial system "reflect its increasing concerns about looming growth headwinds and its increased willingness to step up policy easing and stimulus".
Last week, amid intense pressure from U.S. policymakers including the United States president Donald Trump, the USA central had to step away from its much-debated monetary policy and interest rate hike, despite the inflation target had been closer to central bank's target (1.90 percent while the target was 2 percent).
The US dollar had gained 4.3 per cent in 2018 as the Fed hiked rates four times on the back of a strong domestic economy, falling unemployment and rising wage pressures.
USA 2-year and 10-year Treasury yields fell sharply over the last couple of weeks indicating that bond traders see little chance of the Fed raising rates this year on the increased likelihood of a growth slowdown in the world's largest economy. If the Fed holds rates in 2019, analysts see slim chances of further greenback appreciation.
Global foreign exchange market embraced the first day of the week with bumpy trading as fewer interest rate hikes later would lead to more hot money flowing in the market. The dollar index, a gauge of its value versus six major peers, stood at 96.12 early on Monday, down 0.07 percent.
Chinese stocks firmed after the country's central bank announced an easing in policy on Friday, with 100 basis points of cuts to bank reserve requirements freeing up around $116 billion for new lending.
However, with global stocks largely staying higher amid renewed optimism about a U.S.
The central bank cut interest rates to nearly zero in December 2008.
Goldman Sachs researchers expect a bounce in equity markets in 2019.
The two sides have until March 1 to make a deal, after which Trump has pledged to ramp up tariffs to 25 percent, from 10 percent, on $200 billion worth of Chinese imports.
Spot palladium hit a record high at $1,313.24 per ounce on Monday and was trading at a premium to gold.
The offshore yuan also strengthened on Monday, advancing 0.26 per cent to 6.8483 per dollar, its highest intraday level since Dec 5.