U.S. stock futures rose slightly Tuesday on continued optimism that Greece is nearing a bailout deal with its creditors.

The move higher in futures trading comes a day after a rally across global stock markets that helped propel the Nasdaq Composite to a fresh record.

S&P 500 futures rose 5.5 points, or 0.3%, to 2118. E-mini Dow futures climbed 39 points, or 0.2%, to 18064, and e-mini Nasdaq-100 futures gained 13 points, or 0.3%, to 4546. Changes in stock futures don't always accurately predict moves in the stock market after the opening bell.

European markets rose after Greece's creditors suggested for the first time that a deal to avoid the country's bankruptcy was in sight. Early Tuesday Pierre Moscovici, European commissioner for economic and financial affairs, told French radio France Inter that he expects a deal to be reached this week.

Greek stocks rose nearly 4.5%, while France's CAC 40 and Germany's DAX added 1.3%. On Tuesday Greek stocks jumped 9%, and the CAC 40 and DAX both rallied 3.8%.

Though U.S. stocks have had a strong second quarter so far, with the S&P 500 up 2.7% for the quarter through Monday's close, some investors remain skeptical. U.S. stocks have struggled to break out of a tight trading range so far this year. The S&P 500 had added 3.1% in 2015 through Monday's close, compared with the 6.2% climb the index posted in 2014 through June 20.

"If we have a Greek agreement we could have a continued bounce, but I think once again the market will run out of steam," said Andrew Slimmon, who oversees about $5.3 billion as managing director of Morgan Stanley Wealth Management's Global Investment Solutions. "Historically the market doesn't make a lot of headway in the summer and I don't see why it would be any different this year."

The modest uptick Tuesday morning comes ahead of several economic reports due later in the day. A report on durable goods orders in May is expected at 8:30 a.m. EDT, with economists calling for a decline of 1%. Also scheduled for Tuesday are data on May new home sales.

On Monday, U.S. stocks were lifted by gains in health-care and financial companies.

In commodity markets, gold futures slipped 0.2% to $1182.50 an ounce. Crude-oil futures declined 0.4% to $60.16 a barrel.

Treasury prices fell, pushing the 10-year yield up to 2.394% from 2.362% on Monday. Some investors have been concerned about the health-care sector becoming overheated, as the group has risen more than any other S&P 500 sector in the past year. But ongoing mergers-and-acquisition chatter as well as solid earnings have continued to push shares higher.

"Health care is a very fertile ground for stock-picking," said Mr. Slimmon. "Yes, there are a number of biotech stocks that don't have a lot of earnings that are obviously expensive, but some stocks like Amgen Inc. and Allergan PLC are still attractive."

In corporate news, Darden Restaurants Inc. shares rose 6.7% premarket after the restaurant chain reported across-the-board sales growth and said it plans to create a real-estate-investment trust for restaurants it owns.

Write to Corrie Driebusch at corrie.driebusch@wsj.com

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