Stocks came off session highs in midday trade as investors weighed gains in the dollar and yields, as well as euro zone leaders' remarks on the Greece debt talks.
"We may well be in a position where it's hard to see how optimistic we should be on Greece," said Art Hogan, chief market strategist at Wunderlich Securities.
European equities surged on hopes of resolution in the Greece debt talks, helping Dow futures in the United States gain 150 pionts. The German DAX closed up more than 3.5 percent, while the STOXX Europe 600 gained 2 percent. The ATHEX Composite leaped 9 percent.
"Today is obviously all about Greece and the fact there might be some breaking of the ice," said Ben Pace, chief investment officer at HPM Partners. "Perhaps the market's getting a little ahead of itself because it's just talks, but there's light at the end of the tunnel."
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The Eurogroup of euro zone finance ministers concluded a meeting in Brussels on Monday and will meet again later in the week on the Greek debt crisis. Meanwhile, European Union leaders were set to end an emergency meeting later in the day.
Eurogroup President Jeroen Dijsselbloem said Greece's new proposals are a "welcome step" but not enough to solidify a deal today. Over the weekend, Greece's Prime Minister Alexis Tsipras showed new willingness to make concessions that would unlock aid needed to avoid a default.
Among the more negative comments on the debt talk developments, German chancellor Angela Merkel said in a Reuters report there was no basis on which Greece's creditors could make a decision and that Monday's summit of euro zone leaders was only advisory in nature.
The cash-strapped country faces a 1.5 billion euro ($1.7 billion) payment to the International Monetary Fund (IMF) at the end of the month. If no deal is reached, many speculate Athens will need to impose capital controls to avoid a banking crisis as savers withdraw their bank deposits.
The European Central Bank raised the ceiling on emergency liquidity for Greek banks for the third time in six days, a banking source told Reuters on Monday.
Read MoreGreece gets funding lifeline; crunch talks continue
Peter Boockvar, chief market analyst at The Lindsey Group, said markets should look beyond Greece and focus on the global rise in interest rates.
"For U.S. stocks, I don't think they've blinked much over the past few months over worries with Greece. The euro by the way is flat on the day," he said in a morning note.
The U.S. dollar edged higher, with the euro holding lower $1.134. The U.S. 10-year Treasury yield jumped to 2.37 percent, boosted by optimism on Greece and strong U.S. data.
In economic news Monday, existing home sales jumped 5.1 percent in May to a 5-1/2-year high. Durable goods and new home sales are due Tuesday.
The German 10-year bund yield surged to trade near 0.88 percent. Greek yields on 10-year and 2-year bonds fell sharply from highs hit on Thursday.
Read More Dollar bulls waiting for Greece to subside
Bruce Bittles, chief investment strategist at RW Baird, said the movement in the bond market was partly a reversal of Friday's flight to safety amid uncertainty over Greece.
Outside of Friday's pullback in stocks, Bittles said, "I think the turn came on Thursday, basically when the Fed pretty well assured markets they would remain accomodative." He also cited continued improvement in economic data and investor sentiment.
Stocks rallied last week on the dovish Fed statement, with the Nasdaq Composite topping its high from March 2000 during the tech bubble.