Final answer:
The national government has the power to call out the militia to execute laws and suppress insurrections. Congress has the authority to control the actions of the militia, as outlined in the Constitution.
Step-by-step explanation:
The level of government that has the power to call out the militia to execute laws and suppress insurrections is the national government. According to the Constitution, Congress has the power to call out the militia and control its actions. This power is outlined in Section 8, Clauses 15 and 16 of the Constitution. The National Guard, which is today's equivalent of the militia, can be called into national service by Congress.