More than 1,000 people have been arrested at demonstrations across Russia against President Vladimir Putin's announcement of a partial mobilisation of civilians to fight in Ukraine, a police monitoring group said Wednesday.

The OVD-Info monitoring group counted at least 1,054 people detained at rallies in 38 different cities across the country after Putin's morning address to the nation.

The protests were the largest in Russia since demonstrations that broke out following the announcement of Moscow's military intervention in Ukraine in February.

AFP journalists in the centre of the Russian capital Moscow said at least 50 people were detained by police wearing anti-riot gear on a main shopping street.

In Russia's former imperial capital, Saint Petersburg, AFP reporters saw police surround small a group of protesters and detain them one-by-one, loading them onto a bus.

Protesters were chanting "No mobilisation!"

"Everyone is scared. I am for peace and I don't want to have to shoot. But coming out now is very dangerous, otherwise there would be many more people," said protester Vasily Fedorov, a student wearing a pacifist symbol on his chest.

"I came out to the rally planning to participate, but it looks like they've already arrested everyone. This regime has condemned itself and is destroying its youth," said Alexei, a 60-year-old resident who declined to give his last name.

"Why are you serving Putin, a man who's been in power for 20 years!" a young protester shouted at one policeman.

"I came to say that I am against war and mobilisation," Oksana Sidorenko, a student, told AFP.

"Why are they deciding my future for me? I'm scared for myself, for my brother," she added.

Alina Skvortsova, 20, said she hoped Russians would soon understand the nature of the Kremlin's offensive in neighbouring Ukraine.

"As soon as they really understand, they will come out on to the street, despite the fear," she said.

Defence Minister Sergei Shoigu said Wednesday Russia would initially mobilise some 300,000 reservists, after Putin in a televised address warned Moscow would use all available military means in Ukraine.

Flights out of Russia were nearly fully booked this week, airline and travel agent data showed Wednesday, in an apparent exodus of people unwilling to join the conflict.