Campaigners are urging Facebook to act against what they describe as Russian attempts to silence pro-Ukrainian voices.
They say numerous accounts critical of the Kremlin have been suspended following false reports of abuse filed from Russia.
Ukraine's president has urged Facebook founder Mark Zuckerberg to create a special administrative office to deal with the complaints.
Russia has not commented on the claims.
Addressing Mr Zuckerberg on Facebook, President Petro Poroshenko said: "We have to use all available channels to get reaction from global companies.
"Ukraine does need a Ukrainian Facebook office!"
Underneath, he shared Mark Zuckerberg's status inviting questions for his regular "Townhall Q&A" session on 14 May.
The top responses to Mr Zuckerberg's invitation were overwhelmingly pro-Ukrainian.
"Can you or your team please do something to resolve this problem?" asked the most popular comment, which had attracted more than 41,000 likes at the time of writing.
"Create a separate administration for the Ukrainian segment, block abuse reports from Russia, or maybe just monitor more carefully top Ukrainian bloggers, but somehow help us, please!" it said.
'We make mistakes'
In recent weeks, several prominent Ukrainian users of Facebook have had their accounts suspended after posting updates critical of Russia or Moscow-backed separatists in eastern Ukraine.
A Ukrainian poet, Andriy Bondar, fell foul of the social network's regulations by publishing a verse mocking the Russian media's fixation with Ukraine and referencing the popular hashtag, "What are Ukrainians up to?".
Henadiy Moskal, the plain-speaking governor of the restive Luhansk region, had his Facebook account blocked after sharing a photo of himself standing next to a poster with an obscenity aimed at the separatists.
Russians themselves are not immune from the apparent campaign to silence Kremlin critics on Facebook.
The account belonging to independent journalist Sergey Parkhomenko was suspended on 6 May after he voiced allegations of Russian involvement in the downing of Malaysia Airlines flight MH17 over Ukraine.
Facebook later said this was done in error.
"Our team deals with thousands of reports and complaints on a daily basis, and we make mistakes in rare cases," Russian news agency RBK quoted a Facebook representative as saying.
The Kremlin has not commented on these claims, while Facebook is yet to respond to the calls for a separate administrative office to deal with comments on Ukraine.