(CNN) Some of the active-duty troops who President Donald Trump ordered to help secure the southern border have begun departing and thousands of them could be home by the end of the month, according to a US defense official.

The official said the exact number of troops to stay on the border after the drawdown has not been finalized, but about 2,500 to 4,000 will remain on deployment. That means as many as 2,700 could soon return home.

The border deployment was initially expected to last until December 15 but was recently extended to January 31 following a request from the Department of Homeland Security.

CNN previously reported that the number of troops assigned to the mission would likely drop down to 4,000 as engineers involved in enhancing infrastructure at points of entry completed their tasks.

A separate Defense official says most of the troops to be drawn down will come from Texas.

A Department of Homeland Security official confirmed that some troops will be pulling back, saying it was because of the "requirements of the mission."

Pentagon spokesman Col. Rob Manning said Monday, "Currently, there are approximately 5,200 service members deployed in support of DHS, Customs/Border Patrol along the Southwest border, and the breakdown is as such: 2,200 troops are in Texas, 1,350 troops are in Arizona, and 1,650 troops are in California."

"You asked about when troops will be moving. Some units have completed their mission and have already started to partially redeploy. Other units have been identified to rotate home, and will be returning home over the next several weeks," Manning added.

Trump also deployed some 2,300 National Guard troops to the border as part of an earlier mission. They are scheduled to be there until at least September 2019.

Active-duty troops on the border peaked at about 5,800.

The Associated Press was first to report the drawdown.

The imminent drawdown comes as Trump has publicly weighed having the military construct his sought-after wall along the southern border.

On Tuesday, the President tweeted that the military could build it, should Congress not provide adequate funding.

Later on Tuesday, he clashed publicly with Democratic leaders Rep. Nancy Pelosi, of California, and Sen. Chuck Schumer, of New York, about funding the wall.

Two US officials tell CNN that the National Security Council is planning to hold a Principles Committee meeting Friday focused on border security and the border wall. Secretary of Defense James Mattis is expected to attend.

The chairman of the Senate Armed Services Committee said Tuesday that if Trump can't cut a deal with congressional Democrats to fund construction of a border wall with Mexico, he would be OK if the President cited national security and ordered the military to do it, even without authorization from lawmakers.

Sen. James Inhofe, an Oklahoma Republican, said the main question in his mind is whether the military will have a large enough budget next year for Trump to draw on. He said congressional leaders are waiting to find out how big the defense budget will be, saying the expected range for next year is between $700 billion and $780 billion.

That said, Inhofe also predicted that Trump "probably won't" resort to that step.

The US military has placed concertina wire and repaired some fencing along the southern border using pre-existing funds and authorities.

"To date, there is no plan to build sections of the wall. However, Congress has provided options under Title 10 US Code that could permit the Department of Defense to fund border barrier projects, such as in support of counter drug operations or national emergencies," Lt. Col. Jamie Davis told CNN.

The Pentagon also recently awarded a contract modification in September to conduct an environmental impact study on a potential barrier along the southern boundary of the Barry M. Goldwater Range in Arizona, which abuts some 30 miles of the US-Mexico border.

However, a group of Democratic senators penned a letter Monday to Mattis saying that "assessing further upgrades of that Range's fencing remain a wasteful and unjustified expenditure, which only serves to take away from more important priorities."

The senators said the cost of the assessment was $4.4 million and that a wall along that part of the southern border could run as much as $450 million. A Defense official confirmed the $450 million estimate to CNN.

"Nowhere in the Department's 2019 budget plans was there any proposal to spend nearly half a billion taxpayer dollars to increase security at a bombing range that is already protected by a barrier," wrote Sens. Dick Durbin,Democrat of Illinois, who is vice chairman of the Defense Appropriations Subcommittee; Jack Reed, Democrat of Rhode Island, who is ranking member of the Senate Armed Services Committee; Patrick Leahy, Democrat of Vermont, who is vice chairman of the Appropriations Committee; and Brian Schatz, Democrat of Hawaii, who is the ranking member of the Military Construction and Veterans Affairs Appropriations Subcomittee.

The senators also criticized the Pentagon for saying it was looking at Title 10 authorities pertaining to national emergencies and counter-drug operations.

"We understand that the Department is currently examining other authorities for this roughly $450 million project outside of the budget request process, specifically the potential use of 10 U.S.C. 2808 and 10 U.S.C 284. As you know, outside of a a few small locations requiring security measures for weapons of mass destruction shortly after 9/11, 10 U.S.C. 2808 has never been used inside the United States," the senators wrote.

"We urge you in the strongest possible fashion to refrain from considering using" the authorities pertaining to national emergencies or counter-drug operations "for this potential $450 million border wall project," they added.