Ankara and allied rebels launched operation "Olive Branch" on January 20 against the Kurdish People's Protection Units (YPG), which Turkey has blacklisted as "terrorists".
Afrin's local administration - the semi-autonomous government in place since 2013 - shot back the accusation today and urged Moscow to take a firm stand.
"We ask the Russian Federation in particular to rescind its support for the Turkish state's terrorism against the people of Afrin," it said in a statement.
Russia, which intervened militarily in Syria's war in 2015, had troops positioned in Afrin but withdrew them as Turkey launched the assault.
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The YPG and Afrin officials say that withdrawal amounted to tacit approval of the Turkish offensive.
Officials today also called for the United States, European Union, United Nations Security Council and the US-led coalition fighting jihadists to "immediately intervene to stop Turkey's aggression".
Ankara says it launched the operation to protect its southern border and insists that it is doing everything it can to avoid civilian casualties.
Thousands of people marched to the sound of drums through central Afrin, holding YPG flags and posters of Abdullah Ocalan, the jailed leader of the Kurdistan Workers' Party (PKK).
Turkey is vehemently opposed to the YPG because of its ties to the PKK, which has waged a three-decade insurgency against Turkish forces.
"We're holding the whole world responsible because we fought terrorism on behalf of everyone, but today the world agreed to kill Syrians," said Ali Mahmoud, 45.
Men, women and children thronged main roads in central Afrin for today's demonstration, many chanting slogans.
Some demonstrators clutched olive branches, a symbol of Afrin which is known for its abundant olive groves but which are also now associated with the name Turkey gave its offensive.
"They named their attack 'Olive Branch'. It's a thorn in their hand, but in our hands, it's a gun," said Fikrat Afdal, 33.
At least 68 civilians, including 21 children, have died in Turkish shelling as part of the assault, according to the Syrian Observatory for Human Rights.
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