Opposition figures have complained of threats and harassment.
Kasyanov, a former prime minister turned vocal critic of Russian President Vladimir Putin
, has been targeted repeatedly.
In one incident, caught on camera, he was attacked in a restaurant by two men wielding a cream pie.
In what critics say was another bid to humiliate and discredit the former premier, a secretly-filmed sex tape was also circulated showing the opposition leader in a compromising embrace with a married associate.
The head of the Chechen republic, Ramzan Kadyrov — a key Putin ally — said he posted the clip, insisting it was a joke.
But in a country where critics of the Kremlin are routinely murdered, it is no laughing matter.
Opposition figure killed
In February 2015, another leading Russian opposition figure, Boris Nemtsov, was gunned dow
n on a bridge near the Kremlin, as he walked home from a restaurant.
Kasyanov and Nemtsov
were close associates.
After being released from hospital, Kara-Murza said he believed he had beentargeted by Kremlin supporters
“These days in my country, unfortunately, everyone should be scared about the behavior of the authorities or other people,” Kasyanov told CNN at his party headquarters.
“Me too. I am a normal person, that is why I am also scared and I can expect something to happen to me and my family.”
“But I have to continue this mission, this job, which we are already committed to do,” he added.
Rare television debate
Despite the ratcheting up of pressure on activists, Kasyanov says the current official willingness to allow Kremlin critics to stand for election and be given air time is an opportunity for the political opposition.
He was recently invited to take part in a rare televised debate on state television, where most Russians get their news.