By Sruthi Shankar

European stocks hit their highest level since early March on Tuesday, cementing a rotation into cyclical sectors that helped German shares outperform.

The pan-European STOXX 600 rose 1.6% to notch its strongest close since March 6, while a post-holiday catch up saw Germany's main share index jump 3.8% to its highest in nearly three months.

Volkswagen, Daimler and BMW gained between 5.2% and 7.7% on hopes the German government's proposed 5-billion-euro stimulus package will boost car sales.

Parties in Chancellor Angela Merkel's coalition wrestled on Tuesday over final details of a broader stimulus package to aid the economic recovery from the COVID-19 pandemic.

Europe's automobiles & parts index jumped 3.8%, while insurers, real estate <.SX86P>, oil & gas and banking <.SX7P> sectors rose between 2.9% and 3.9%.

The growth-sensitive sectors have recovered since mid-May on the back of improving economic data as lockdown restrictions across the world ease, helping the STOXX 600 index climb nearly 34% from a March trough.

The European Central Bank is also set to meet on Thursday, with policymakers expected to ramp up bond purchases.

The broad optimism helped investors look past rising U.S.-China trade tensions and the worst civil unrest in the United States in decades.

"There continues to be a push and pull battle raging in stock markets with the technical position winning again in May," wrote Roger Jones, head of equities at London & Capital.

"This created positive returns but the fundamental outlook still looks extremely fragile and uncertain."

Lufthansa shares gained 3.4% as its supervisory board approved a 9-billion- euro government bailout even as it forced the German airline to give some of its prized landing slots to rivals.

France's biggest private TV operator TF1 jumped 6.7% as it announced the launch of a new soccer channel 'Telefoot' along with its partner MediaPro Group.

Norway's Seadrill sank 15.0% after writing down $1.2 billion on the value of its oil drilling rigs and warning that it may have to convert a part of its $7.4 billion in debt into equity to survive.

(Reporting by Sruthi Shankar in Bengaluru; Editing by Arun Koyyur and Emelia Sithole-Matarise)