Equities on both sides of the Atlantic advanced amid speculation Greece and its international lenders will reach a deal soon that would safeguard the euro.
The Stoxx Europe 600 Index ended the day with a 0.6 percent gain from the previous close. Germany's DAX Index rose 0.9 percent, while France's CAC 40 Index added 1 percent. Greece's Athens Stock Exchange General Index jumped 8 percent.
"Anything that makes us believe we can avoid a sloppy Greek exit is going to be a positive for markets overall, and that is where we are at right now," Art Hogan, chief market strategist at Wunderlich Securities in New York, told Reuters.
The European Commission denied reports it will present a compromise proposal at the meeting on Wednesday, saying "very intense contacts are ongoing between" Commission President Jean-Claude Juncker, Greek Prime Minister Alexis Tsipras and others, and that the plan being worked on is to keep Greece in the euro area, Bloomberg Business reported.
Wall Street also rose. In afternoon trading in New York, the Dow Jones Industrial Average advanced 0.52 percent, the Standard - Poor's 500 Index gained 0.67 percent, while the Nasdaq Composite Index climbed 0.91 percent.
Gains in shares of Coca-Cola and those of Pfizer, up 2.8 percent and 2.5 percent respectively, helped propel the Dow higher. Shares of Chevron and Exxon Mobil were the biggest percentage decliners in the Dow, recently 0.9 percent and 0.8 percent weaker respectively.
Shares of Coca-Cola gained after the company reported quarterly profit that bettered estimates.
Coca-Cola earnings were "slightly better than expected, due to good cost management and more reasonable commodity costs,'' Jack Russo, an analyst at St. Louis-based Edward Jones - Co, told Bloomberg Business. Still, 2015 remains a year of transition, he said. ''Slowing emerging market growth and the strength of the US dollar will meaningfully impact 2015 earnings-per-share results.''
Thomson Reuters data through Tuesday morning showed 72.7 percent of the 341 S-P 500 companies that have reported topped earnings expectations, above the 69 percent beat rate in the past four quarters.
Meanwhile, Chevron and Exxon Mobil slid with the price of oil after the International Energy Agency said US output is continuing to rise.
"It's the battle of the oil outlooks playing out here," John Kilduff, partner at New York energy hedge fund Again Capital, told Reuters. "The IEA report is a good reminder that there's still a lot of supply to come and it doesn't give much hope for the bulls who say we've hit bottom and are now on the way up."
The latest US economic data did not alter the view that the economy remains solid.
A Commerce Department report showed wholesale inventories increased 0.1 percent in December, while a Labor Department report showed said job openings climbed to 5.03 million in December, the highest level since January 2001.
Separately, a report by the National Federation of Independent Business showed its small business optimism Index declined 2.5 points to 97.9 in January.
"The labour market is shifting into overdrive with jobs out there for nearly everyone. The litmus test for whether or not the expansion is on track and a solid one is always jobs creation," Chris Rupkey, chief financial economist at MUFG Union Bank in New York, told Reuters.