Army Secretary Ryan McCarthy told AP that the reversal came after Esper attended a meeting at the White House.
Esper broke his lengthy silence regarding the surge of protests nationwide following the May 25 death of George Floyd.
The Army announced that female soldiers will be integrated into all of its infantry and armor BCTs by the end of the year.
The officials said that about 200 soldiers with the 82nd Airborne's immediate response force will be the first to leave.
The House passed a bill on cost-of-living increases in veterans benefits for 2021.
The Pentagon has ordered a battalion of military police soldiers from Fort Bragg to deploy to the Washington, D.C. area.
According to the National Park Service, several memorials across Washington, D.C., were vandalized.
Wright noted that racism, discrimination and exclusion "does not care much about position, titles or stature."
A soldier fired three rounds at a speeding vehicle deemed a threat, officials said.