NATO Secretary-general Anders Fogh Rasmussen on Wednesday asked for greater Russian assistance for the Western military alliance's operations in Afghanistan, but received no immediate promise of more help from Moscow.

Making his first visit to Moscow since taking office in August, Rasmussen met with a series of senior Russian officials in his latest effort to lubricate NATO-Russia ties that were strained in the wake of the Caucasus war last year.

At a meeting with Rasmussen, President Dmitry Medvedev said that Russia's relations with NATO are entering a new stage.

"We have many reasons for interaction, many subjects for discussion," including joint actions to counter terrorism, crime and other common threats, Medvedev said.

He expressed the hope that Rasmussen's visit would help make Russia-NATO ties "stronger and more productive."

Rasmussen, in his turn, admitted differences in NATO-Russia relations, but said they should not overshadow common interests in many fields.

The Russian president missed no opportunity to urge NATO to mull over Russia's proposal to map out a new European security treaty.

Medvedev in late November sent a draft treaty on European security to leaders of others countries and international organizations of the Euro-Atlantic space. But the initiative has so far received a lukewarm response from the West.

Speaking to reporters after the Kremlin meeting, Rasmussen said he has presented Russian leaders with a list of "concrete proposals" on rendering NATO more assistance in Afghanistan.

"I have invited Russia to step up its terms of cooperation in Afghanistan," the Danish NATO chief said, adding that Russia could contribute by supplying helicopters, spare parts and fuel, and by training pilots.

Rasmussen stressed that Russia's cooperation on NATO's war effort in Afghanistan is beneficial to both sides. "I do believe that it's essential for Russia that we succeed in Afghanistan," he said.

"If Afghanistan once again becomes a safe haven for terrorists, then Russia would be among the first victims, as terrorists could easily spread from Afghanistan through Central Asia to Russia," Rasmussen said.

Foreign Minister Sergei Lavrov, who had met with Rasmussen earlier in the day, said after the Kremlin talks that the president had instructed the government to study the NATO chief's proposals.

Rasmussen later also held talks with Prime Minister Vladimir Putin, who said he hoped for less contradictions between Russia and NATO in the future.

"A unification of Russian and NATO efforts in spheres of common interests may yield good results," Putin said.

Although Russia and NATO hold different views on various issues, they continue to cooperate in the combat against terrorism, expansion of weapons of mass destruction, drug trafficking and organized crime, the premier added.

Relations between the military bloc and Moscow have improved recently after being frozen for months.

Rasmussen, who has made ties with Moscow a priority since he assumed the post, was reported to be seeking to transport lethal cargoes by railroad across Russia to Afghanistan.

Russia has allowed the transit of non-lethal supplies for NATO and U.S. troops in Afghanistan through its territory under an April 2008 deal signed in Bucharest.

Rasmussen told the Ekho Moskvy radio station late Wednesday that NATO has not asked for Moscow's permission to use its territory for the overland transit of military supplies to Afghanistan.

However, he acknowledged that NATO is interested in expanding cooperation with Russia on Afghanistan, including the transit of the alliance's cargoes.