London's benchmark FTSE 100 index edged up 0.06 percent to 6,302.97 points compared with Monday's close.
In the eurozone, Frankfurt's DAX 30 eased 0.10 percent to 9,805.41 points and the Paris CAC 40 dipped 0.14 percent to 4,610.43.
European stock markets had surged higher on Monday as weak US jobs data fuelled expectations that the US Federal Reserve would not hike interest rates this year.
London and Frankfurt both jumped by 2.7 percent and Paris soared 3.5 percent on Monday.
US stocks also powered higher Monday, while on Tuesday in Asia equities won support also from agreement on a Pacific-wide free-trade agreement.
After five years, trade representatives from 12 nations on the Pacific Rim said Monday they had finally hammered out a deal to create the world's biggest free trade area -- encompassing 40 percent of the world economy.