"They [Russians] are members of our Assembly, as well as the Ukrainians are members of the Assembly. It's only through dialogue that we can find a solution, not through violence," Brasseur said as the winter session of PACE closed on Friday.
At the same time, the PACE president underlined that the assembly had maintained the sanctions imposed against the Russian delegation last April because "we maintain that the territorial integrity of Ukraine must be respected."
In light of Crimea's reunification with Russia in March 2014, in April PACE suspended Russia's voting rights until the end of the year, which led to the Russian delegation walking out of the spring session and skipping the summer session in protest.
Brasseur noted that even after the sanctions were imposed against the Russian delegation last year, she had tried to maintain contact with the chairman of the Russian parliament Sergei Naryshkin and had met him three times during 2014.
"We [Brasseur and Naryshkin] spoke to each other, we listened to each other, but we could not understand each other, or come to a conclusion," Anne Brasseur said.
She underlined the credentials of the Russian delegation will be the subject of another debate at the next session in April.
On Wednesday, PACE adopted an amendment restricting Russia's right to vote and participate in the work of the Council of Europe until April 2015, accusing Moscow of meddling in the military conflict in the southeast of Ukraine.
Moscow denies any direct involvement in the Ukrainian crisis, other than helping to bring the warring parties to the negotiation table.