The Dow Jones Industrial Average gained 37.32 points (0.28 percent) about an hour into trade.

The broad-market S&P 500 gained 5.75 points (0.40 percent) to 1,436.11, while the tech-rich Nasdaq Composite climbed 19.12 points (0.64 percent) at 3,029.73.

On Monday, US President Barack Obama and top Republican John Boehner made strides towards a deal to avert the year-end tax and spending crisis -- the so-called fiscal cliff -- that experts warn could spark a recession.

Obama and Boehner appeared to have reached a compromise on the income level to be affected by the White House push to raise taxes on the rich.

"The market appears taken with the idea that new proposals are at least being advanced by both sides that differ from prior versions, suggesting last week's stalemate in the negotiation process has ended," said Briefing.com's Patrick O'Hare.

Apple increased 0.9 percent. Late Monday, a US judge denied the tech giant's request to ban a set of Samsung smartphones from the US market after a jury found the South Korean electronics titan guilty of patent infringement.

Morgan Stanley gained 2.2 percent. The bank agreed Monday to pay a $5 million fine to settle charges that it improperly handled crucial information on Facebook's earnings ahead of the company's disastrous IPO. Facebook was up 1 percent.

Media audience ratings service Nielsen rose 1.4 percent after announcing it will buy Arbitron to expand its radio ratings for $1.26 billion in cash. Arbitron soared 23.5 percent.

Bond prices fell. The 10-year US Treasury yield increased to 1.78 percent from 1.76 percent late Monday, while the 30-year climbed to 2.95 from 2.93 percent.

Bond prices and yields move inversely.

On Monday, the Dow added 0.76 percent, the S&P 500 rose 1.19 percent and the Nasdaq Composite climbed 1.32 percent.