One protester Brian Elliot spoke to the Edinburgh Evening News, saying: “I spoke to officers [on Tuesday] and they were happy with us protesting.
"Then, [Wednesday] we’re not allowed to hang our signs up outside and we’ve had to move further down the road.
"They said because the situation in Ukraine is changing all the time, the advice they’re being given is changing.”
Although they have not had to move far, protesters have been told they are no longer allowed to stand, or put their signs up, right outside the front of the consulate.
Mr Elliot said: “It restricts our right to protest.”
Police Scotland have said they need to balance the right of the protesters with the legal obligation to maintain access to the building.
Protesters will now be situated further down the street rather than directly outside the front of the building.
Superintendent David Robertson said: "Police Scotland is a rights-based organisation that puts our values of integrity, fairness, respect and a commitment to upholding human rights at the heart of everything we do.
"We will provide a proportionate policing response to any protest and will engage with those taking part to ensure their rights to peaceful assembly and protest are protected.
"When protests take place outside a consulate, we will balance the rights of those who wish to protest with our legal obligation to maintain access to the building."