Australian Daniel Ricciardo led the field for Red Bull, with Dutch team mate Max Verstappen at the back after crashing in qualifying.
Germany's Nico Rosberg, the world championship leader, has won the last three Monaco Grands Prix for Mercedes and qualified second.
With cars trailing around behind the safety car for the first seven laps, some drivers began to sound impatient.
"The spray's better now, let's get going," Mercedes's triple world champion Lewis Hamilton said over the team radio on lap five before the signal came that the safety car would be brought into the pits.
It came in but the virtual safety replaced it within a lap after Renault's British rookie Jolyon Palmer crashed out at Sainte Devote, scattering debris across the track.
(Reporting by Alan Baldwin, editing by Clare Fallon)
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