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May 11 (Reuters) - European shares were muted on Monday, as stalled U.S.-Iran peace negotiations pushed oil prices higher and weighed on risk appetite.

The pan-European STOXX 600 .STOXX was flat at 611.67 points, as of 0703 GMT. Regional bourses moved in different directions, with London's FTSE 100 .FTSE adding 0.2%, while France's CAC 40 .FCHI dipped 0.5%.

U.S. President Donald Trump rejected Iran's response to a U.S. peace proposal, calling it "totally unacceptable." Tehran proposed ending the war on all fronts, including Lebanon, along with compensation for war damage and claimed sovereignty over the Strait of Hormuz, Iranian state TV said.

The war has shuttered the Strait of Hormuz, a vital waterway for a fifth of global oil and liquefied natural gas flows, with soaring oil prices adding to concerns over the conflict's impact on inflation and growth.

Energy-dependent Europe remains vulnerable, with markets still trading below pre-war levels.

Among early movers, UK's Compass Group CPG.L gained 3.8% after the world's largest caterer raised its full-year profit outlook.

Shares of Delivery Hero DHER.DE rose 3.7% after Dutch technology investor Prosus PRX.AS sold a 5% stake in the German food-delivery group to activist investor Aspex Management for roughly 335 million euros ($393 million).