Russian men of fighting age should not be allowed to travel abroad, a senior lawmaker was quoted as saying on Monday, amid growing public concern that wider border closures will be announced to stop people fleeing the draft.

“Everyone who is of conscription age should be banned from travelling abroad in the current situation,” Sergei Tsekov, a member of Russia’s upper house of parliament, the Federation Council, told RIA news agency.

Since President Vladimir Putin announced a partial call-up of reservists to fight in Ukraine last week, flights to leave the country have sold out and protests have been staged – and swiftly broken up by police – in cities across Russia.

The announcement triggered panic that men of fighting age would be turned away at the borders, although the Kremlin has dismissed reports of people fleeing to airports.

Another lawmaker played down the idea of border closures and said the government was providing support measures to those being called up to serve.

“I would like to invite all colleagues (instead of inflaming the situation) to pay attention to the issues of social support for citizens who are subject to mobilisation…,” Andrei Klishas, another member of the Federation Council, wrote in response to Tsekov’s proposal.