"It's clear," an official said yesterday on condition of anonymity.
London, Paris and Washington had asked that the request be put on hold as they sought additional information on the shipments.
They also called on Russia to strengthen measures related to the storage of the weapons in the Central African Republic, which has been under an arms embargo since 2013.
"Our only request was that the Russian delegation submit additional information on the serial numbers of the weapons... so that we can track weapons going into CAR," said a US official.
The Central African Republic's leaders asked Russia several months ago to provide weapons for units being formed by the EU.
Moscow wants to equip two battalions totalling 1,300 men. Among the weapons to be shipped are 900 pistols, 5,200 assault rifles, 140 sniper rifles, 840 Kalashnikov machine guns, 270 RPGs and 20 anti-aircraft guns.
France blocked a previous request last month over concerns about the storage of the weapons in the volatile country, a council diplomat said.
It also wants to train troops on use of the weapons, another proposal subject to the UN's green light.
In the long term, the UN's peacekeeping forces in the Central African Republic must be replaced by the country's own armed forces.
The Central African Republic has faced instability since it exploded into violence after the 2013 overthrow of longtime leader Francois Bozize by the mainly Muslim Seleka rebel alliance.
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