In London, one of dozens of events across Europe, tens of thousands demonstrated, brandishing placards reading "Open the Borders", an AFP journalist said, while in Copenhagen, some 30,000 took to the streets.
"I want to support the refugees. We admire your bravery. You deserve a safe and happy life. We welcome you here with open arms," said Deborah Flatley in London, holding a homemade cardboard sign reading:
In Berlin, demonstrators waved a Syrian flag with "Refugees Welcome" written on it, while rallies in Stockholm, Helsinki and Lisbon each attracted around 1,000 people, including at a picnic in the Finnish capital.
But highlighting how the arrival of hundreds of thousands of migrants has divided the European Union, there were counter-demonstrations in eastern members of the bloc.
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"We're here so that the government hears our voice and abandons any plans to welcome Muslims," the organiser of one such protest in Warsaw told a crowd of around 5,000 people chanting anti-Islam slogans.
The influx has exposed deep rifts with the EU, with "frontline" states Italy, Greece and Hungary struggling and European Commission proposals for sharing 160,000 of the new arrivals in a quota scheme facing resistance among eastern members.
Germany has absorbed the lion's share so far, taking in 450,000 people with the government of Chancellor Angela Merkel -- hailed as a heroine by many migrants but under fire at home, even from allies -- relaxing asylum rules for Syrians.