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(CNN) —  

President Donald Trump said Thursday he was considering sending “anywhere from 2,000 to 4,000” National Guard troops to the southern border, applying the first figures to his surprise announcement this week that military forces will be deployed to bolster security.

Trump said the administration is still looking at how much the deployment might cost, but that he has a “pretty good idea.”

And he insisted the troops would remain there until his proposed border wall is complete.

The remarks answered, at least in part, several outstanding questions about the deployment plan, which Trump first announced on Tuesday.

Additionally, the Department of Defense announced Thursday that the National Guard’s efforts for border security will include “aviation, engineer, surveillance, communications, vehicle maintenance and logistics support.”

“These National Guard members will act in support of Border Patrol agents who are performing law enforcement duties,” Chief Pentagon spokesperson Dana White said in a statement.

Administration officials admitted to being caught off-guard by the President’s declaration during a lunch with Baltic leaders that “we’re going to be guarding our border with the military.”

The White House could not answer questions about the size, cost or length of the deployment over the past two days.

The range of troops that Trump revealed on Tuesday falls within historic precedent. President George W. Bush sent 6,000 National Guard troops to assist with border security in 2006. And President Barack Obama sent 1,200 in 2011.

The two operations cost more than $1.3 billion combined.

CNN’s Sophie Tatum contributed to this report.