"I would love to believe that following the recent UK tragedy principles of the European policy, according to which the cooperation with Russia in fight against terrorism was minimized, will be revised," Kosachev wrote on Facebook.
The Russian lawmaker stressed that decreasing the level of cooperation with Moscow was at least a mistake and even "an assistance to common enemies."
"I do not think that it is time to talk about omissions of the UK security services… It is obvious that no one created an absolute protection from terror. However, the only way to defeat terrorism is to begin defeating it. Step by step, in a joint and coordinated way," Kosachev added.
"It is time to understand that it is not [Syrian President Bashar] Assad, the Kremlin, Tehran or Washington who blows up the Europeans. Our proposal on cooperation and formation of the anti-terrorist coalition remains vital and indefinite," Kosachev said.
Russian President Vladimir Putin has long called for the creation of a broad international coalition to fight terrorism, particularly the Islamic State terror group, which is outlawed in many countries, such as Russia and the United States, including at the UN General Assembly in September 2015.
Nations around the globe strive to counter the increasing terror threat via all available means, including adoption of additional security measures.