Source: Sharecast
Stocks across London, Frankfurt and Madrid gained 0.4-0.5%, while Milan's index jumped 0.9% and Paris and Zurich both surged 1.2%.
As a result, the Stoxx 600 index finished the day 0.7% higher at 558.06, having gained 4.2% since the start of the month.
The last time the index closed higher was 3 March when it reached an all-time high of 563.13.
Trump and European leaders in Washington claimed Russia leader Vladimir Putin had agreed to meet face-to-face with Zelenskyy to thrash out a peace deal, although there was no confirmation from Moscow. Zelenskyy and the leaders of France, Germany and UK pressed for US-backed security guarantees as part of any long-term agreement.
"Stocks across the region edged higher, with sentiment boosted by the apparent progress in discussions between Presidents Trump and Zelenskyy, along with European leaders," said David Morrison, senior market analyst at Trade Nation.
"The focus remained firmly on diplomatic efforts to halt the Russian war with Ukraine, though investors stopped short of pushing prices sharply higher."
In other news, traders were keeping a close eye on developments at the Jackson Hole Economic Symposium, looking for hints to just what Federal Reserve chairman Jerome Powell will look to do at the Fed's remaining policy meetings this year.
Market movers
Limiting upside across Europe were big falls in the defence sector as arms and equipment manufacturers plunged amid fears their wares may not be in as much demand as first thought.
Shares in Renk Group, Babcock, Saab AB, Kongsberg Gruppen, Leonardo, Dassault, Thales, Qinetiq, Rheinmetall and Hensoldt all finished with heavy losses.
Leading the upside on the Stoxx 600 was UK retailer JD Sports after Deutsche Bank upped its price target on the stock to 100p from 85p, citing improving trends for Nike.
Anglo American also headed higher after saying it was seeking damages after American peer Peabody pulled out of a $3.8bn deal to take over its steelmaking coal business in Australia.
Luxury stocks Burberry, Moncler, Swatch, LVMH and Christian Dior were also performing well.