UPDATE 2-German stocks outpace rest of Europe as cyclicals jump

(For a live blog on European stocks, type LIVE/ in an Eikon news window)

* German carmakers jump on report of buyer bonus scheme

* Worries over U.S.-China tension, U.S. protests persist

* Norway's Seadrill slides on $1.2 billion asset writedown

(Updates to market close)

By Sruthi Shankar

June 2 (Reuters) - 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 .STOXX rose 1.6% to notch its strongest close since March 6, while a post-holiday catch up saw Germany's main share index .GDAXI jump 3.8% to its highest in nearly three months.

Volkswagen VOWG_p.DE , Daimler DAIGn.DE and BMW BMWG.DE gained between 5.2% and 7.7% on hopes the German government's proposed 5-billion-euro ($5.6 billion) stimulus package will boost car sales. 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. automobiles & parts index .SXAP jumped 3.8%, while insurers .SXIP , real estate .SX86P , oil & gas .SXEP 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. 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 LHAG.DE 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. biggest private TV operator TF1 TFFP.PA jumped 6.7% as it announced the launch of a new soccer channel 'Telefoot' along with its partner MediaPro Group. Seadrill SDRL.OL 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. ($1 = 0.8945 euros)