At a Pentagon briefing earlier, Esper said the Insurrection Act should only be used in dire emergencies.
Mattis charged that President Donald Trump has failed in his duties to the Constitution and the American people.
Phil Roe said he supports a gender-neutral version of the VA's mission statement.
Wright was the first member of senior military leadership to speak out publicly following the May 25 death of George Floyd.
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.