The announcement came two days after a Spanish judge sent a new request to international police agency Interpol demanding their arrest.
"We consider compliance with international arrest warrants to be mandatory, and we must proceed with immediate implementation by the Salvadoran authorities," Salvador's human rights ombudsman David Morales said late
In 2011, the former soldiers evaded a Spanish order for their arrest by taking refuge in military barracks in San Salvador.
They also secured a ruling from El Salvador's Supreme Court saying they were protected by an amnesty that pardoned the atrocities committed during the 1980-1992 civil war.
But this time, Morales urged the High Court to "proceed immediately to ensure the arrest of the accused."
Spanish High Court Judge Eloy Velasco has reissued the orders for the arrest of the former soldiers.
They include Colonel Inocente Montano, a former vice minister of public safety who is serving a 21-month sentence in the United States for immigration fraud.
Morales urged the United States to allow his extradition to Spain.
He also called on the military to "abstain" from blocking the arrest of the former soldiers.
Five of the priests killed in November 1989 were Spanish and one was Salvadoran. The soldiers also killed the priests' housekeeper and her daughter.