Donald Trump is poised to start withdrawing troops from the US-Mexico border as early as this week, according to a report that prompted instant criticism that their deployment was a political stunt.

The US president spent the final weeks of the midterms election campaign whipping up fears of a migrant caravan travelling through Mexico towards the border. He sent in about 5,900 troops to prevent the “invasion” but, once polls closed, talked far less about the issue.

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On Monday the Politico website reported that the Pentagon is planning to begin a drawdown of the troops.

Army lieutenant-general Jeffrey Buchanan, overseeing the mission, said the first troops will start heading home in the coming days as some are already unneeded, having completed the missions they were sent for, Politico reported.

“The returning service members include engineering and logistics units whose jobs included placing concertina wire and other barriers to limit access to ports of entry at the US-Mexican border,” the website added.

Facebook Twitter Pinterest Soldiers work on installing concertina wire at the US-Mexico border. Photograph: Thomas Watkins/AFP/Getty Images

Buchanan, based in Texas, added that the active-duty troops sent to assist Customs and Border Protection (CBP) at the border should be home by Christmas. “Our end date right now is 15 December, and I’ve got no indications from anybody that we’ll go beyond that,” he was quoted as saying.

Trump’s decision to deploy troops at the border provoked a fierce backlash from commentators who regarded as it a blatant use of the military for electoral gain.

On Monday, three critics with military and national security experience – Gordon Adams, Lawrence Wilkerson and Isaiah Wilson III – wrote in the New York Times: “The president used America’s military forces not against any real threat but as toy soldiers, with the intent of manipulating a domestic midterm election outcome, an unprecedented use of the military by a sitting president.”

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Trump’s apparent move now to withdraw them also caused criticism. Norman Ornstein, a resident scholar at the American Enterprise Institute thinktank in Washington, tweeted: “Troops at border starting to withdraw. Proving again that this was a blatant misuse of our military and tax dollars for partisan political purposes by Trump.”

Ornstein expressed disappointment that Jim Mattis, the defence secretary, had gone along with the plan.

The Pentagon declined to confirm the Politico report. Laura Seal, a spokeswoman, said: “The assistance we are providing to CBP at the south-west border has been authorised through December 15. While we have made significant progress in closing gaps and hardening points of entry, I don’t have any redeployment details to announce at this time.”

Around 3,000 people from the first of the caravans have arrived in Tijuana, Mexico, across the border from San Diego, California. It is the busiest border crossing between the two countries, with about 110,000 people entering the US every day in 40,000 vehicles.

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On Monday, the US closed off northbound traffic for several hours to install new security barriers. The US secretary of homeland security, Kirstjen Nielsen, said that the lanes had been closed temporarily, claiming that border patrol officials had been notified that “a large [number] of caravan migrants were planning to rush the border in an attempt to gain illegal access to the US”.

She provided no further information or evidence for the claim and David Abud, a representative from Pueblos Sin Fronteras, the organisation coordinating the caravan, said: “Secretary Nielsen’s false comments about the refugee exodus are a deliberate attempt to mislead the public and demonise refugees fleeing government-sponsored violence and displacement.”

In protests on Sunday, about 400 Tijuana residents waved Mexican flags, sang the Mexican national anthem and chanted “Out! Out!” referring to the caravan that arrived in the border city last week. Trump tweeted: “The Mayor of Tijuana, Mexico, just stated that ‘the City is ill-prepared to handle this many migrants, the backlog could last 6 months.’ Likewise, the U.S. is ill-prepared for this invasion, and will not stand for it. They are causing crime and big problems in Mexico. Go home!”