European stocks close higher as Brexit concerns ease

European stocks closed mostly higher on Tuesday following polls that allayed fears of a Brexit, however, a renewed decline in oil prices added pressure to the market.

The pan-European STOXX 600 ended the day around 0.9 percent higher, reversing earlier losses. Most sectors, apart from Basic Resources and Telecoms, were in positive territory.

The U.K.'s FTSE 100 ended the day up 0.7 percent, while its European counterparts, the French CAC and German DAX popped 0.9 and 0.8 percent respectively.

Global markets rallied on Monday after several opinion polls over the weekend showed that the "Remain" camp was regaining momentum ahead of the referendum on Britain's European Union membership on Thursday.

Polls released Monday evening for The Telegraph newspaper and The Times showed conflicting voter intentions, however. The pound was trading higher at $1.471, up from levels of around $1.40 last week. 

But with markets becoming sensitive to opinion polls on the referendum, there are concerns a sharp sell-off could occur if opinion polls turn again to show a swing in favor of the leave camp.

"Financial markets appear to be taking the view that the race may well already be run, which given the twists and turns seen already in this campaign may well be extremely far sighted, or dangerously premature," Michael Hewson, chief market analyst at CMC Markets, wrote in a Tuesday note. "With more polls due out later today we can expect to see further volatility unfold in the event of a move either way."

Elsewhere, Germany's constitutional court, the top court in the country, ruled that the European Central Bank's (ECB) Outright Monetary Transactions (OMT) program was not illegal and can be used. The OMT gives the ECB the power to buy the debt of struggling euro zone members. 

And the German ZEW institute's economic sentiment index for June came in at 19.2, a big rise from the 6.4 recorded in the previous month, giving a boost to investor sentiment.  

In markets overseas, U.S. stocks opened slightly higher, while Asia markets closed mixed, as investors awaited news from the EU referendum debate, and kept an eye on the oil price. 

Oil prices fell in trade on Tuesday as the market turned cautious and focused on supply issues, following a strong two-day rally fed by easing Brexit concerns. Investors were also eyeing reports from Nigerian media which suggested that the government had signed a 30-day ceasefire with militants, according to Reuters. 

Brent and U.S. crude were off some 2 percent each, trading around $49.65 and $48.40 respectively. Meanwhile, metal prices also dipped, capping gains in the basic resources sector. ArcelorMittal and Anglo American were among some of the sector's worst-performers.

And BHP Billiton was lower after an update in which it explained plans to boost coal output and cut costs. A fall in the price of gold also put pressure on precious resource miners Fresnillo and Randgold Resources which were trading in the red. 

In individual stock news, French telecoms operator Bouygues was trading higher after Kepler Cheuvreux raised the rating on the stock from "reduce" to "buy". 

Shares of Whitbread—the owner of Premier Inn and Costa—pared sharp gains but remained higher, after the firm said sales rose 8 percent in the first quarter. Meanwhile, KION Group was at the bottom of the benchmarks, after the German manufacturer announced it was buying Dematic, in a deal valuing the logistics technology firm at $3.25 billion; Reuters reported. Shares sank over 7 percent.

Elsewhere, public pension fund Boston Retirement System, filed a bondholders class action lawsuit against Volkswagen claiming that the German carmaker's "false and misleading statements and omissions" cause its bonds to trade at "artificially inflated prices" and fall after the emissions scandal became public. Volkswagen shares were trading in the red.

The banks were one of the best sector performers, up some 1 percent. Shares of France's Credit Agricole were sharply higher after it said on Tuesday that 83 percent of its shareholders elected to receive their dividend in the form of shares. 

Italy's Banca Popolare di Milano (BPM) is to cut its stake in asset manager Anima Holding. BPM would have had to launch a full takeover bid for Anima under Italian regulation because of the size of the stake it owned in the company. If it cuts it stake, it won't have to do this. Shares of BPM were up some 1.5 percent.

And Banco Popolare soared over 3 percent, after it sold around 152 million euros ($172.46 million) worth of non-performing loans to Banca Ifis. 

Follow CNBC International on Twitter and Facebook.