The FTSEurofirst 300 slipped at the open, after stocks gained in Asia and on Wall Street on Monday.
The yen gained but stayed below recent peaks against the dollar and gold, also sought in times of market tension, fell.
Russian President Vladimir Putin signed an order approving a draft treaty on "adopting the Republic of Crimea into the Russian Federation". He was due to address a special joint session of the Russian parliament on the issue later, aides said.
Ukraine's mainly Russian-speaking region of Crimea voted overwhelmingly in a weekend referendum, condemned by Western states, in favour of joining Russia.
In the wake of Sunday's vote, the United States and the European Union imposed sanctions on a small group of Russian and Crimean officials. However, markets' worst fears that the referendum would lead to violence were not realised.
"The sanctions taken against Russia are relatively soft, and there has been no real escalation in the tensions in the past week, which is good news," Talence Gestion fund manager Alexandre Le Drogoff said.
"Overall, the market has been quite resilient in this Ukrainian crisis, but now it needs a positive catalyst to resume its rally, and we might have to wait for first-quarter corporate results for that."
Russia's stock market, hammered in the run-up to the vote, edged higher, though the rouble fell 0.8% to 36.58 to the dollar.
Earlier, MSCI's broadest index of Asia-Pacific shares outside Japan added about 0.3%. Japan's Nikkei stock average ended up 0.9%, recovering from Monday's six-week closing low.
The S&P 500 index rebounded on Monday from its worst weekly fall in the past seven, ending 0.96% higher as concerns eased over Ukraine and after data indicated the US economy was improving after a winter slowdown.
US manufacturing output posted its biggest rise in six months in February and this was expected to encourage the Fed to announce it will further scale back its monetary stimulus after its two-day policy meeting ends on Wednesday.
Policymakers could adopt less specific language to describe conditions under which it might tighten policy, instead of the bank's current threshold of a 6.5% unemployment rate. The rate stands at 6.7%, though Fed officials are still signalling that rates need to stay low to support the economy.
OIL RISES
The yen gained almost 0.4% to 101.40 to the dollar but stayed below peaks around 101.20 hit last week. The euro held steady around $1.3940, not far from a 2 1/2-year high around $1.3967 touched on Thursday.
"In immediate focus is ... Putin's speech later today. If he plays down an immediate annexation of Crimea by Russia, the dollar could gain further ground on unwinding of risk aversion," said Masafumi Yamamoto, chief strategist at Praevidentia Strategy in Tokyo.
China's yuan fell against the dollar on China's problems with a slowing economy and heavily indebted corporate sector. Spot yuan traded at 6.19 to the dollar, compared with 6.1781 at Monday's close.
German 10-year government bond yields, the euro zone benchmark, edged lower. Yields on US 10-year Treasuries, which rose on Monday after the US data, fell 2.1 basis points to 2.68%.
Spot gold traded at $1,360.56 an ounce, having hit a six-month high of $1,391.76 on Monday before profit taking kicked in.
Brent crude oil edged above $106 a barrel as bargain hunters stepped in after prices fell $2 on Monday on the reduced Ukraine tensions.
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