NATO on Thursday said Russia had been fully informed about a cooperation agreement signed in late September by the alliance and the United Nations, reported dpa.
"We briefed the Russians on a regular basis on this. Everybody in the UN knew. We don't understand their concern at this stage," NATO spokesman James Appathurai told reporters on the sidelines of a NATO defence ministers' meeting in Budapest.
Russian news agency Itar-Tass quoted Russian Foreign Minister Sergei Lavrov as expressing "surprise" at what was being described by the Russian media as "a secret deal".
NATO says the agreement signed in New York with the UN merely formalizes cooperation between the two institutions in crisis regions such as Afghanistan and Kosovo, and will not bring about any "dramatic changes".
But Lavrov complained on Thursday about provisions in the text, which he said had not yet been made public.
"We were surprised that the very text of the agreement, which has not yet been placed on the UN and NATO websites ... contains a provision on prerogatives of member-states," Lavrov was quoted as saying.
According to Russia's ambassador to NATO, Dmitry Rogozin, Moscow is worried that the cooperation agreement could lead to NATO taking over the role of the UN in some areas.
"In principle, we do not object to UN-NATO cooperation, but NATO should fully acknowledge thhe UN's universal role and not try to substitute UN functions," Rogozin said.
The row comes at a delicate time for NATO-Russia relations following the August conflict in Georgia.
NATO allies have decided to suspend regular meetings of the NATO-Russia council, which provides a forum for direct dialogue between the sides, because of Russia's "disproportionate use of force" and its violation of Georgia's territorial integrity.
Diplomats say a resumption of the council meetings is not expected yet, despite reports that Russia has pulled its troops out of core Georgia ahead of an internationally-agreed deadline.
NATO defence ministers were due to hold talks with their Georgian colleague in Budapest on Friday.
The alliance is providing support to Georgia's military, but will not supply any weapons.
Georgia has been promised it will be able to join NATO at an unspecified future date. That offer has infuriated Moscow, which does not want to see the US-dominated alliance extend its influence in former Soviet territory.