They voted 4-1 late Tuesday to authorize the county manager to negotiate a purchase of the building, which lies just off Civic Plaza, on Copper between Second and Third streets.
The decision is not final. An agreement to buy First Plaza must come back to the County Commission for approval.
The county has been trying for years to find an office building where it can consolidate the employees and offices now scattered among a half-dozen sites in the Downtown area.
Commissioners didn’t explain their decision Tuesday, except to note that a final decision will come later.
Lonnie Talbert, a Republican, was the lone “no” vote.
The First Plaza building has 316,000 square feet of space. Built in 1972, it’s shaped like a horseshoe.
It’s available for $13 million, with 150 parking spaces, according to county documents.
But the price could be reduced to $11 million if the county agrees to trade four of the buildings it owns now: The Rio Grande Building at Fifth and Tijeras, Union Square by the railroad tracks, and the old courthouse and old jail.
The county estimated last year that it could sell the Downtown buildings it already owns for about $11 million. That would include selling its interest in the City Hall and Government Center complex, which it shares with Albuquerque’s municipal government and the water authority.
The county has also been considering sticking with what it has now, buying the Alvarado Square building, or studying the possibility of a joint venture with a private developer to build something new.