The Frankfurt stock market gained 0.03 per cent, London rose 0.15 per cent, Madrid increased 0.02 per cent and Paris added 0.23 per cent, as European investors gave their first tentative reaction.
Japan's Nikkei index turned in the strongest showing, up nearly one per cent amid a report showing that the country's exports rose for the seventh straight month in June.
Other major indexes - including Hong Kong's Hang Seng and South Korea's Kospi - were up, but not as vigorously.
'Pinch of salt'
But some analysts said the assessments were not tough enough and questions remained over the true health of the sector.
"On the surface, if anything, you have to take these tests with a pinch of salt," Jonathan Cavenagh, a currency strategist at Westpac, Sydney, said.
"Sovereign debt problems remain, funding constraints for their banks are still there and these have the potential to weigh on the euro."
Steven Leung, director of institutional sales at UOB-Kay Hian China's policy on credit and earnings reports out of the US this week would be the driving factors in the week's market performance.
"This week, we are watching for another round of earnings out of the US. People are waiting for another round of signals."
US stocks were expected to fall on opening on Monday amid a slew of earnings reports. Dow futures were down by 0.3 per cent to 1,097.20 and the broader S&P 500 futures were lower by 0.3 per cent to 1,097.20.