Trading volumes are generally expected to remain lower than normal, given the holiday in the US markets.
The Stoxx 600 index of European shares rose 0.8%, following falling last week, on fears of a global economic slowdown.
The euro zone banks index fell 0.4% following a media report indicated that the European Central Bank would consider depriving banks of exceptional profits estimated at billions of euros while raising interest rates.
Shares of British energy giant BP jumped 3.6%, leading the gains of European oil and energy companies.
The shares of travel and leisure companies came following oil and gas companies, with gains of 1.3 percent.
Shares of Grafton Group fell 5.9 percent, following the company that specializes in building materials announced that its CEO, Gavin Slark, would step down from his 11-year position.
Japanese shares rose at the close on Monday, supported by utility companies, as the country continues to face an unprecedented heat wave.
Overall, investor sentiment remained low, due to widespread fears of a global economic slowdown, with trading slowing ahead of the US Independence Day holiday, Monday.
The Nikkei index rose at the closing 0.84% to 26153.81 points, following it briefly declined below the psychological level of 26000 points in the morning session.
The broader Topix index rose 1.34% to 1869.71 points.
The Nikkei posted a weekly loss of 3.01% on Friday, while the Topix fell 2.08%.
The utilities sector rose 4.11%, making it the best performing sector in the Nikkei, with Tokyo Electric Co. up 12.95%.
Mitsubishi shares rose 3.98%, following falling 5.21% last week.
And shares of SoftBank Group, the technology giant, increased by 2.96%, following recording a weekly decline of more than six percent. (Archyde.com)
European stock markets rose on Monday, boosted by oil and gas stocks, while investors awaited the release of inflation data in the euro zone, following a report on consumer prices published last week boosted expectations that the European Central Bank would raise interest rates.