Insurrection: A Quick Reference
Dealing with insurrection is provided for by the laws of the United States--specifically in Title 10, Chapter 13. I'm not making any recommendation here, just providing a handy reference point so you'll know what laws are in play. Fortunately, these laws are very short and to the point.
Here's an article that deals with insurrection in a general way, addressing the two most pressing questions--Can the president respond to civil insurrection with military force? and What are the rules for the use of force? The President, the Military and Minneapolis: What You Need to Know . The 25 words or less version: Yes; but the JCS would need to issue Standing Rules for the Use of Force, which would stop short of aggressive use of deadly force against looters. That doesn't address the use of life threatening violence by insurrectionists. Informative
251.1 - Federal aid for State governments.
252.1 - Use of militia and armed forces to enforce Federal authority.
253.1 - Interference with State and Federal law.
254.1 - Proclamation to disperse.
255. - Guam and Virgin Islands included as "State".
§251. Federal aid for State governments
Whenever there is an insurrection in any State against its government, the President may, upon the request of its legislature or of its governor if the legislature cannot be convened, call into Federal service such of the militia of the other States, in the number requested by that State, and use such of the armed forces, as he considers necessary to suppress the insurrection.
§252. Use of militia and armed forces to enforce Federal authority
Whenever the President considers that unlawful obstructions, combinations, or assemblages, or rebellion against the authority of the United States, make it impracticable to enforce the laws of the United States in any State by the ordinary course of judicial proceedings, he may call into Federal service such of the militia of any State, and use such of the armed forces, as he considers necessary to enforce those laws or to suppress the rebellion.
§253. Interference with State and Federal law
The President, by using the militia or the armed forces, or both, or by any other means, shall take such measures as he considers necessary to suppress, in a State, any insurrection, domestic violence, unlawful combination, or conspiracy, if it—
(1) so hinders the execution of the laws of that State, and of the United States within the State, that any part or class of its people is deprived of a right, privilege, immunity, or protection named in the Constitution and secured by law, and the constituted authorities of that State are unable, fail, or refuse to protect that right, privilege, or immunity, or to give that protection; or
(2) opposes or obstructs the execution of the laws of the United States or impedes the course of justice under those laws.
In any situation covered by clause (1), the State shall be considered to have denied the equal protection of the laws secured by the Constitution.
§254. Proclamation to disperse
Whenever the President considers it necessary to use the militia or the armed forces under this chapter, he shall, by proclamation, immediately order the insurgents to disperse and retire peaceably to their abodes within a limited time.
§255. Guam and Virgin Islands included as "State"
For purposes of this chapter, the term "State" includes Guam and the Virgin Islands.