By Saumya Vaishampayan And Dan Strumpf 

U.S. stocks fell Tuesday, as European officials met to hash out what could be a final push to keep Greece in the eurozone.

The Dow Jones Industrial Average slipped 39 points, or 0.2%, to 17646 shortly after the opening bell, while the S&P 500 lost three points, or 0.1%, to 2066. The Nasdaq Composite Index declined 17 points, or 0.3%, to 4976.

The eurozone's top decision makers met Tuesday and pushed for new bailout proposals from Greek Prime Minister Alexis Tsipras after his voters overwhelmingly rejected creditors' austerity measures in Sunday's referendum. Officials warned that a solution won't come immediately. A summit of European leaders will follow a meeting of the currency union's finance ministers.

Greece and its creditors are racing against the clock before Greek banks run out of cash, which could further weigh on the country's struggling economy and pave the way for an exit from the euro. The country faces a July 20 deadline to make a EUR3.5 billion bond repayment to the European Central Bank. Greece's banks and stock market remained closed.

"Right now, there's hope that we can get back to the negotiating table and get something done," said Art Hogan, chief market strategist at Wunderlich Securities.

European stocks were mostly lower. France's CAC-40 fell 1.1% and Germany's DAX lost 0.9%.

Tuesday's declines followed losses on Monday, though the losses weren't as steep as many had expected following Sunday's referendum in Greece. The Dow lost 0.3% while the S&P shed 0.4%.

In the coming weeks, investors will turn their focus to the stream of second-quarter earnings reports from U.S. companies. The earnings season unofficially kicks off Wednesday afternoon with Alcoa Inc.'s second-quarter report. Quarterly profits for S&P 500 companies are forecast to decline 4.5% for the quarter, according to FactSet. That would mark the first decline since the third quarter of 2012. Analysts similarly predicted a decline ahead of first-quarter earnings, but profits ended up rising by 0.8%.

Chinese stocks fell Tuesday, raising concerns about the government's ability to stem the slide. The Shanghai Composite declined 1.3%.

In commodity markets, gold futures lost 1.4% to $1157.30 an ounce. Crude-oil futures fell 2% to $51.38 a barrel.

The yield on the 10-year Treasury note declined to 2.208% from 2.280% on Monday. Yields fall as prices rise.

In corporate news, Allergan PLC said it reached a deal to buy the exclusive rights to two experimental migraine drugs from Merck & Co. for $250 million. Allergan shares fell 0.2% while Merck shares gained 0.1%.

Write to Saumya Vaishampayan at saumya.vaishampayan@wsj.com and Dan Strumpf at daniel.strumpf@wsj.com