President Trump is significantly expanding the National Guard’s presence at Washington, D.C., with troop numbers set to double in the coming days as multiple states commit to sending additional service members to bolster patrols.

As many as 1,000 troops from the states of Mississippi, West Virginia, Ohio, and South Carolina will be sent to the nation’s capital to bolster the presence of National Guard members who have remained mainly idle in areas of the city with low crime rates and high tourism.

Governors from the cadre of states said they were responding to the Trump administration’s requests to join the operation. The administration has not explained why it requested additional military support. About 800 troops from the Washington, D.C., National Guard have already been deployed with limited roles in Mr. Trump’s effort to federalize law enforcement in the district.

“Crime is out of control there, and it’s clear something must be done to combat it,” Mississippi’s governor, Tate Reeves, said in a statement on Monday. His state was the latest to answer the call, following suit with the other three states whose Republican governors made pledges over the weekend to send troops.

Some GOP governors have pushed back and decided to keep their troops home, including Vermont’s Phil Scott.

“While public safety is a legitimate concern in cities across the country and certainly in the nation’s capital, in the absence of an immediate emergency or disaster that local and regional first responders are unable to handle, the governor just does not support utilizing the guard for this purpose, and does not view the enforcement of domestic law as a proper use of the National Guard,” Mr. Scott’s chief of staff, Jason Gibbs, said in a statement to Vermont Public.

The White House recently announced that some of those stationed at Washington would begin carrying firearms, a reversal of the initial deployment orders.

In a statement released on Saturday, White House officials said National Guard troops stationed at Washington “may be armed, consistent with their mission and training, to protect federal assets, provide a safe environment for law enforcement officers to make arrests, and deter violent crime with a visible law enforcement presence.”

D.C.’s mayor, Muriel Bowser, has called for more honesty about the operation, saying officials must acknowledge it’s not just about curtailing crime but about immigration enforcement — a centerpiece of Mr. Trump’s second term. At a news conference on Monday, she challenged Mr. Trump’s characterization of the city and questioned the administration’s true intentions.

“I think it makes the point that this is not about D.C. crime,” she said. “The focus should be on violent crime. … Nobody is against focusing on driving down any level of violence.”

“And so, if this is really about immigration enforcement, the administration should make that plain.”