The ambassadors will discuss the crisis in Ukraine as well as Afghanistan's security, and terrorism in the region, a NATO official said.
"Following consultations with the members of the NATO-Russia Council (NRC), I have invited them to a meeting at ambassadorial level," NATO chief Jens Stoltenberg said in a statement.
"The meeting will take place on 30 March at NATO headquarters in Brussels," he added.
The NRC had met regularly until the Ukraine crisis plunged relations with Moscow into the deep freeze in 2014, though this will be the fourth meeting since the forum resumed nearly a year ago.
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US-led NATO has suspended all practical cooperation with Russia over its role in Ukraine but Stoltenberg has said political channels of communication have always remained open.
Russia's ambassador to NATO Alexander Grushko and alliance counterparts will also discuss "military activities, reciprocal transparency and risk reduction in order to improve stability and security in the Euro-Atlantic area," the NATO official said on condition of anonymity.
The meeting comes on the eve of Tillerson's visit to Brussels for consultations with the other foreign ministers of the 28-nation alliance.
Tillerson's decision to skip the initial NATO meeting and visit Moscow the same month instead also fuelled concerns among the alliance about Trump's admiration for Russian President Vladimir Putin.