"The center will ensure a prompt and effective response to terrorist threats against Russian installations, agencies or nationals outside the Russian Federation," said Nikolai Patrushev, who is also NAC chairman.
He said the proposal will be considered at an upcoming session of the Federal Operations Headquarters in July.
The Federal Security Service (FSB) chief also said an international antiterrorism center could be created in the Caucasus.
"We will continue to work along these lines," he said.
He said 72 organizations involved in financing terrorist activities were closed down in Russia in 2006.
"We probed last year over 1,000 organizations and 3,000 individuals in a search for financial sources of terrorism," Nikolai Patrushev said, adding that over 50 criminal cases were launched as a result of the probe and 17 extremist organizations banned.
He said Russian security services had foiled terrorist attacks during a G8 summit in St. Petersburg in 2006, and the Russia-EU summit in Sochi earlier this year.
"Preventive measures helped deter [Chechen] warlords' plans to carry out terrorist acts and damage Russia's reputation on the international stage," Patrushev said.
He said 546 militants had surrendered since an amnesty was declared in the North Caucasus last July, adding that a new amnesty could be granted to Chechen militants who lay down their arms.
Patrushev said 30 terrorist attacks in southern Russia have been foiled so far this year.
Deputy Prosecutor General Ivan Sydoruk said Thursday police had disarmed 148 members of illegal armed groups, and killed 39 militants since the start of the year. However, he said the situation in the North Caucasus remains difficult, with heavy casualties among law enforcers.
Since the start of the year, "45 law enforcement officers have been killed and another 55 policemen wounded in Chechnya and Dagestan," the official said.
Sydoruk said 11 extremist crimes have been reported in the Southern Federal District since the beginning of January, 20% more than in the same period of last year.
The Astrakhan Region, the Krasnodar, and Stavropol territories reported the most disturbing results, he said.
