Britain has circulated a draft resolution that would set up the new political mission and the council is scheduled to vote on the measure on July 10.
The council last year set up a first mission to oversee disarmament of the leftist rebels. On Tuesday, that was completed when the last of some 7,000 weapons were handed over.
With that phase of the accord completed, UN envoy Jean Arnault told the council that the "first and most urgent challenge" was now the reintegration of 10,000 combatants of the Revolutionary Armed Forces of Colombia (FARC) into society.
Both the Colombian government and the FARC rebels have asked the Security Council to authorize the new mission, Arnault said.
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The British-drafted resolution would establish the new UN presence "to verify the FARC's political, social and economic reintegration, and also implementation of their security guarantees," said a Security Council diplomat who asked not to be named.
It would ask UN Secretary-General Antonio Guterres to provide a report to the council in August with detailed recommendations on how the mission should work.
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