European stock markets continued to climb Tuesday after hitting multiyear highs in the previous session, with investors encouraged by European parliamentary e lection victories for governing parties in Germany and Italy.

The Stoxx Europe 600 was 0.3% higher by midmorning, while Germany's DAX added 0.5% and the U.K.'s FTSE 100 climbed 0.6%, in a move that strategists deemed to be catch-up play after a public holiday in the U.K. and U.S. on Monday.

The broadly bright start to the week suggests that investors aren't concerned by the strong electoral performance by euroskeptic parties, particularly in France and the U.K.

"Financial markets were prepared for these results, and a strong showing for Matteo Renzi's Democratic Party, as well as Angela Merkel's CDU, helped spur the euro to gains, while equity markets rallied and peripheral bond spreads (notably Italian government bonds) tightened," Kit Juckes, a macro strategist at Société Générale, wrote in a note to clients.

Strategists at Barclays meanwhile, said that they don't expect the election results to trigger any major change in policy, but added that "the confidence crisis in European institutions will have to be taken seriously by the next Parliament and Commission."

Deutsche Bank economist Jim Reid wrote in a note that the outcome was "more of an embarrassment to the mainstream rather than something for markets to get very concerned about."

He did, however add that in the longer term, it highlights how quickly and unexpectedly fringe parties can gain traction.

"This will be a continuing story bubbling up in the background but one that markets will probably largely ignore until it is more imminent," he added.

The upbeat sentiment looked to be reflected in the U.S. too, with futures indicating a 0.5% rise for the S&P 500. Changes in futures, however, aren't necessarily reflected in market moves after the opening bell.

In Europe, France's CAC-40 was the only major index not to gain. It hovered around the previous day's level, after data confirmed that the country remains the laggard of the European recovery.

Consumer confidence stagnated at a historically low level in May, coming in at 85, unchanged from April and well below the long-term average of 100.

Earlier this month, data showed that the French economy failed to grow on a quarter-on-quarter basis during the first three months of the year, after expanding just 0.2% in the final quarter of last year.

In currency markets, the euro was little changed against the U.S. dollar at 1.3644. Japan's yen was broadly flat too, at 101.93 against the dollar. Stocks in Tokyo hit a seven-week high Tuesday, led by key exporters.

Russian stocks dropped Tuesday, wiping out the gains seen Monday after Ukraine's presidential election at the weekend yielded results broadly in line with expectations.

Dozens of pro-Russian separatists were killed by Ukrainian soldiers in heavy fighting at a key regional airport that is now back under government control, Ukraine's interior minister said Tuesday.

Rebel fighters took over Donetsk International Airport early Monday leading to a fierce battle as government forces deployed helicopters, fighter jets and paratroopers to regain control of the building. It was the first heavy fighting to hit the capital city of Ukraine's industrial heartland since the crisis in eastern Ukraine began in March. The Micex and RTS were down 3.4% and 2.9% by mid-morning respectively while the ruble continued to lose ground against the U.S. dollar, to hit 34.379.

In commodities markets, gold dipped 0.7% to $1,283.80 an ounce, while Brent crude oil dropped 0.5% to $109.81 a barrel.

Trade in Europe will likely be kept thin by the Ascension Day holiday in some countries in the region on Thursday.