Kochneva, a 40-year-old Ukrainian citizen, was abducted in October by Syrian rebels as she travelled to the city of Homs, and has been held there by them since, they claim.
Ukraine's foreign ministry urged Damascus to step up its effort to ensure her release.
The rebels responded with a video threatening to target the embassies of Ukraine and Russia and their citizens.
"Let not a single Russian, Ukrainian or Iranian come out of Syria alive," the rebels said in the video broadcast by Ukraine's Ukraina TV channel Wednesday.
Kochneva's kidnappers have threatened to kill her Thursday if their demand for a $50 million ransom is not met, several journalists' support groups including the Committee to Protect Journalists (CPJ), Reporters Without Borders, and press freedom group ARTICLE 19 said in a statement.
The NGOs, who say she is being held by the Free Syrian Army, called on the US and EU states to help with negotiations to facilitate Kochneva's release, in a statement on the ARTICLE 19 website.
Kochneva, known as an expert on Syrian affairs, has been in Syria since the start of the conflict.
An outspoken supporter of President Bashar al-Assad, she was freelancing for several Russian media outlets, including the NTV, RenTV and RT channels and Utro.Ru news portal.
After she was kidnapped in October, she appeared in a YouTube video in which she confessed to working for Russian intelligence. Her captors claim Koncheva was armed and had acted as an interpreter for Russian officers.
Both Iran and Russia remain among the few countries supporting the Assad regime.
Since the beginning of the Syrian conflict, 17 journalists and 48 citizen-journalists have been killed, while 21 journalists and 18 citizen-journalists remain imprisoned by the Syrian government, according to Reporters without Borders.
Moscow: Syrian rebels behind the kidnapping of Ukrainian journalist Ankhar Kochneva have released a video threatening more attacks on Russians and Ukrainians, as the deadline for her execution approached Thursday.
First Published: Friday, December 14, 2012, 00:37