The pan-European STOXX 600 index added 0.9%, with German stocks up 1% and France's CAC 40 0.8% higher.
Having led the recovery from March's pandemic-driven lows, technology shares <.SX8P> were the day's best performers, mirroring gains on Wall Street.
Heavyweight German enterprise software maker SAP SE rose 2.2% after U.S. peer Salesforce.com raised its 2021 revenue forecast.
Germany's coalition parties agreed to extend measures to cushion the economic effects of the coronavirus crisis at a cost of up to 10 billion euros, while France is set to present its economic recovery plan on Sept. 3.
"This is an important sign for investors, as another standstill of the European economy would have devastating consequences," said Milan Cutkovic, Market Analyst at AxiCorp.
"The coordinated response of the European Union to the Corona crisis has also strengthened confidence."
Caution was, however, still evident as COVID-19 cases on the continent continued to rise and two confirmed cases of coronavirus re-infections in Europe raised concerns about immunity to the virus.
Markets were also waiting for U.S. Federal Reserve Chairman Jerome Powell's speech on Thursday, which could offer further cues on the U.S. economic recovery.
Economic data in the past week has muddied the outlook for the euro zone recovery, keeping the STOXX 600 in a holding pattern about 15% below its all-time high, even as U.S. stocks hit new peaks on easing U.S.-China trade tensions and hopes of a coronavirus treatment.
"We've had a disappointing set of flash PMIs last week, which gives you an impression that after the initial rebound, the recovery is going to stall," said Andrea Cicione, head of strategy at TS Lombard.
Swedish radiation therapy equipment maker Elekta topped the STOXX 600 after posting a bigger-than-expected first-quarter profit.
HiQ International soared nearly 26% after private equity firm Triton announced a 3.9 billion crown ($444.92 million) cash bid for the Swedish IT consultancy firm.
Telecom Italia rose 5.1% after a local newspaper reported the Italian government had given approval to U.S. investment firm KKR to buy a minority stake in its secondary grid.
Ambu, which makes diagnostic and life-support devices for hospitals, slumped 13.4% after it cut its full-year earnings forecast.
(Reporting by Sruthi Shankar in Bengaluru; editing by Uttaresh.V and Shailesh Kuber and Kirsten Donovan)
By Sruthi Shankar and Ambar Warrick
