* NATO to review cooperation with Russia by early April
* Areas include Afghanistan mission, counter-narcotics, piracy
* Cuts back lower-level contacts, mission planning
By Justyna Pawlak
BRUSSELS, March 5 (Reuters) - NATO announced a full review of its cooperation with Russia on Wednesday to try to pressure Moscow into backing down on Ukraine and said it would suspend planning for a joint mission linked to Syrian chemical weapons.
NATO Secretary-General Anders Fogh Rasmussen said alliance officials would no longer hold lower-level meetings with their Russian counterparts, while stepping up engagement with the civilian and military leadership of Ukraine, not a NATO member.
"We have also decided that no staff-level civilian or military meetings with Russia will take place for now," Rasmussen told reporters after a meeting between NATO and Russian officials in Brussels.
"The situation in Ukraine presents serious implications for the security of the Euro-Atlantic area," he said.
NATO has been in talks with Russia on a possible joint mission to protect the U.S. cargo ship Cape Ray that will destroy Syria's deadliest chemical weapons.
Under a U.S.-Russia deal reached after a chemical attack killed hundreds of people around Damascus last year, Syrian President Bashar al-Assad's government should have handed over 1,300 tonnes of toxic chemicals by Feb. 5 for destruction abroad.
NATO's ties with Russia have improved since the Cold War ended but deteriorated following the defence alliance's eastward expansion to take in former Communist-ruled countries in eastern Europe and Moscow's war in Georgia in 2008.
The alliance briefly suspended formal cooperation on security threats after the war but resumed it in 2009.
Since then, it cooperates with Moscow in a range of areas, including the alliance's military mission in Afghanistan, in counter-narcotics projects in Afghanistan and in combating terrorism and piracy.
Diplomats said it would be difficult for the 28-nation alliance to cut back ties in Afghanistan as NATO prepares to end combat operations there by the end of 2014 amid a fragile security situation.
Any decisions will likely be taken at the next meeting of NATO foreign ministers at the start of April in Brussels and depend on whether tensions between Russia and Ukraine have subsided.
Russia's envoy to NATO accused the alliance of applying double standards and "Cold War" stereotypes to Russia after the NATO announcement.
"This meeting proved that NATO still has a double standard policy. And Cold War stereotypes are still applied towards Russia," Alexander Grushko told reporters.