Europe closes higher as hopes for Greek deal rise

European equities closed higher Tuesday as the countdown to a potential debt deal between Greece and its creditors continued.

The pan-European Stoxx 600 index closed around 1.2 percent higher Tuesday, with all sectors ended the day in positive territory.

U.S. stocks, meanwhile, traded in narrow range on Tuesday as investors digested mixed economic reports for indications on the timing of a rate hike.

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Flash data released Tuesday morning showed that the composite purchasing manager's index (PMI) for the euro zone in June rose to 54.1, up from 53.6 in May - a 49-month high for the index by Markit that surveys activity in the region's services and manufacturing industries.

The French CAC index closed around 1.2 percent higher, after composite PMI data for the country rose to 53.4 in June, up from a final reading of 52.0 in May.

The German DAX also closed higher at 0.7 percent, while the London FTSE 100 index closed just 0.1 percent higher.

In individual stocks news, Delhaize Group closed near the top of the Stoxx 600 at 8.4 percent, after supermarket group Ahold said it was in the "final stages" of merger talks. Ahold ended the day 1.8 percent higher.

Sports Direct finished at the top of the FTSE 100 index, as RBC Capital Markets lifted its rating on the apparel retailer to outperform.

Greek hopes

Markets continue to hope that Greece will come to some kind of reforms-for-rescue deal with its international creditors this week, after Athens presented a new set of reform proposals Monday. Greece owes the IMF 1.6 billion euros on June 30 and could default on the debt without more aid.

Read MoreGreece divided over reforms and future

The reforms were presented to euro zone finance ministers and leaders at a set of emergency summits in Brussels Monday.

"I am convinced that we will come to a final agreement in the course of this week," European Commission President Jean-Claude Juncker told a late-night news conference.

But German Chancellor Angela Merkel struck a more cautious note, saying she couldn't give "any guarantee" that an agreement would come.

At the close on Tuesday, the euro continued to show signs of weakness against the dollar, down 1.35 percent at $1.118.