U.S. stocks rose on Tuesday following back-to-back daily declines, with merger activity more than offsetting market concerns as Greece struggles to avoid a default on its debt.

Traders also kept an eye on interest rates as a two-day policy-setting meeting at the Federal Reserve got under way.

Despite the collapse of talks between Athens and its European and IMF lenders over the weekend, Greek Prime Minister Alexis Tsipras told U.S. Treasury Secretary Jack Lew that Athens aimed to reach a deal. Lew said failure to reach an agreement would create broad uncertainties for the global economy.

"The market seems to be pricing in a possibility, overpricing, a Greece exit," said Art Hogan, chief market strategist at Wunderlich Securities in New York.

He said he does not expect a surprise to the market from the Fed in terms of a rate hike, or from a Greek default.

"Financials have been leading and dividend payers have sold off. That trade probably unwinds if there is a surprise," he said.

The Dow Jones industrial average .DJI rose 113.31 points, or 0.64 percent, to 17,904.48, the S&P 500 .SPX gained 11.86 points, or 0.57 percent, to 2,096.29 and the Nasdaq Composite .IXIC added 25.58 points, or 0.51 percent, to 5,055.55.

Stocks had opened lower but quickly turned higher and drifted up throughout the day to close near the session's high.

Consumer staples lead the way up, with Coty (COTY.N) shares at a record, closing up 19.3 percent at $31.08. Coty is on track to buy Procter & Gamble's (PG.N) beauty business in a $12 billion deal. P&G shares closed up 1.3 percent at $79.10.

In other merger news, shares of NCR Corp (NCR.N) hit a 14-month high of $36.50. Reuters reported Blackstone (BX.N) and Carlyle (CG.O) are making a joint bid for NCR in what would be the year's biggest leveraged buyout at more than $10 billion, including debt. NCR closed up 10.7 percent at $34.73 while Blackstone fell 0.6 percent to $41.98 and Carlyle rose 0.8 percent to $28.41.

The chance that the Fed Wednesday will give more clarity on the timing of its expected rate hike was seen as a catalyst for more takeover deals.

"Rising rates could be a trigger for even more M&A activity," said Brian Jacobsen, chief portfolio strategist at Wells Fargo Funds Management in Menomonee Falls, Wisconsin.

"They are a signal that now's the time to get the deals done if you are going to do them with cheap financing."

Advancing issues outnumbered declining ones on the NYSE by 1,946 to 1,104, for a 1.76-to-1 ratio on the upside; on the Nasdaq, 1,635 issues rose and 1,158 fell for a 1.41-to-1 ratio favoring advancers.

The benchmark S&P 500 index posted 8 new 52-week highs and 4 new lows while on the Nasdaq Composite there were 138 new highs and 37 new lows.

About 5.5 billion shares changed hands on U.S. exchanges, below the 5.98 billion daily average so far this month, according to BATS Global Markets.