The Dow Jones Industrial Average added 93.33 points, or 0.53 percent, to 17,776.91. The S&P 500 gained 12.58 points, or 0.61 percent, to 2,081.34. The Nasdaq Composite Index edged up 5.52 points, or 0.11 percent, to 4,997.46.
An emergency Eurogroup meeting in Brussels, Belgium, on the Greek debt deal ended inconclusive Tuesday afternoon, with lenders saying publicly that their expectation for new Greek proposals fell, but Athens denied.
The finance ministers of eurozone countries didn't receive new proposals they had expected from Greece Tuesday, said Eurogroup head Jeroen Dijsselbloem after the crucial meeting.
Newly-appointed Greek Finance Minister Euclid Tsakalotos gave an oral presentation to the eurozone finance ministers, saying the new proposal would be presented Wednesday.
The statements from both sides were made as Greek Prime Minister Alexis Tsipras was holding a meeting with German Chancellor Angela Merkel and French President Francois Hollande in Brussels ahead of the eurozone summit which was convened later Tuesday on the Greek issue.
Greek banks are closed and capital controls have been imposed in Greece since June 29. ATMs are expected to run out of cash this week, and without emergency assistance, Greece seems to be heading to default and possibly an exit from the eurozone.
On economic front, the goods and services deficit of the United States was 41.9 billion U.S. dollars in May, an increase of 1.2 billion dollars from April's revised level, according to the U.S. Commerce Department Tuesday.
The number of job openings was little changed at 5.4 million on the last business day of May, the highest since December 2000, the Department of Labor reported Tuesday.
The CBOE Volatility Index, often referred to as Wall Street's fear gauge, shed 5.41 percent to end at 16.09 Tuesday.
In other markets, oil prices continued to drop as investors awaited developments in the Greek debt crisis.
The West Texas Intermediate for August delivery moved down 0.20 dollar to settle at 52.33 dollars a barrel on the New York Mercantile Exchange.
The U.S. dollar increased against the euro as investors were awaiting future developments in Greek debt crisis.
In late New York trading, the euro fell to 1.0977 dollars from 1.1051 dollars in the previous session, while the dollar bought 122.46 Japanese yen, higher than 122.45 yen of the previous session.
Gold futures on the COMEX division of the New York Mercantile Exchange fell as investors waited to see if a eurozone summit could produce results in alleviating the debt crisis in Greece.
The most active gold contract for August delivery lost 20.6 dollars, or 1.76 percent, to settle at 1,152.60 dollars per ounce.