The Nikkei index of the Tokyo Stock Exchange climbed 124.69 points to 8,803.58 hours after European leaders voiced confidence about their progress towards a resolution of the problem.
The Topix of all first section shares also rose 1.14% or 8.47 points to 752.68.
However, a lack of specific details from the eurozone talks has seen investors remain relatively cautious, said Kenichi Hirano, operating officer at Tachibana Securities.
"Caution nevertheless remains as nothing concrete has yet been decided," he told Dow Jones Newswires.
European leaders, including French President Nicolas Sarkozy and IMF chief Christine Lagarde, yesterday said "good progress" had been achieved on talks to overcome their debt crisis that has threatened the world economy.
However, they announced few concrete details, vowing to reveal all at a second summit on Wednesday.
Ahead of the weekend, optimists pushed up global shares Friday, sending the Dow Jones Industrial Average to close up 267.01 points, or 2.31%, to 11,808.79.
The broader S&P 500 added 1.88%, while the tech-heavy Nasdaq Composite rose 1.49%.
The market gains in Tokyo came despite the yen's continued strength, which hurts Japan's exporters. The currency hit a fresh record of 75.78 to the dollar during New York trade Friday.