Donald Trump said on Tuesday he will deploy the US military to guard the border with Mexico, adding: “That’s a big step.”

The president was speaking to reporters at the White House, around a meeting with leaders of Baltic countries. Administration officials had earlier responded to the president’s continued Twitter offensive on the subject of immigration by telling media they were crafting a new legislative package aimed merely at closing immigration “loopholes”.

“We are going to be guarding our border with our military,” Trump said. “That’s a big step.

“We cannot have people flowing into our country illegally, disappearing, and by the way never showing up for court.”

At a subsequent press conference, Trump said: “We are preparing for the military to secure our border between Mexico and the United States. We have a meeting on it in a little while with [defense secretary] Gen Mattis and everybody and I think its something we have to do.”

Earlier, Trump had resumed a Twitter offensive on immigration begun on Sunday.

“The big Caravan of People from Honduras, now coming across Mexico and heading to our ‘Weak Laws’ Border, had better be stopped before it gets there,” he wrote. “Cash cow NAFTA is in play, as is foreign aid to Honduras and the countries that allow this to happen. Congress MUST ACT NOW!”

Trump also tweeted about “caravans” on Sunday and Monday, while declaring protections for so-called Dreamer migrants “dead”; accusing Democrats of allowing “open borders, drugs and crime”; and warning Mexico to halt the passage of immigrants or risk US abandonment of the North American Free Trade Agreement (Nafta).

“Nafta has been a terrible deal for the United States,” Trump told reporters on Tuesday, adding that a renegotiated deal would still be good for Mexico.

Trump’s tweets about migrant “caravans” followed a Fox & Friends report on Sunday that featured the leader of the border patrol agents’ union. About 1,100 migrants, many from Honduras, have been marching along roadsides and train tracks in the southern Mexican state of Oaxaca.

Such “Stations of the Cross” caravans have been held in southern Mexico for at least the last five years. They began as short processions of migrants, some dressed in biblical garb and carrying crosses, as an Easter-season protest.

Individuals often try to reach the US border but usually not as part of caravans, which typically do not proceed much further north than the Gulf coast state of Veracruz. The current march was scheduled to end this month with a conference on migration in the central state of Puebla.

On Monday night, the Mexican government said it had stopped the caravan. “Under no circumstances does the government of Mexico promote irregular migration,” a statement said.

“[Mexico] did it because you really have to do it,” said Trump on Tuesday, adding: “If [the caravan] reaches our border our laws are so weak and so pathetic … it’s like we have no border.

“The caravan doesn’t irritate me, the caravan makes me very sad that this could happen to the United States. President Obama made changes that basically created no border.”

Trump reiterated his complaints about the caravans, Nafta and immigration law in the Tuesday press conference.

Trump has been seething – and preaching to his political base – since realizing the major spending bill he signed last month barely funds the “big, beautiful” border wall he promised supporters and repeatedly said Mexico would pay for. The $1.3tn funding package included $1.6bn in border wall spending, but much of that money can be used only to repair existing segments.

“We need to have a wall that’s about 700 to 800 miles” of the border, he told reporters on Tuesday. At the press conference he insisted the wall had begun to be built, a misleading claim he has made before.

Though the spending bill was widely seen as the last major legislation to pass this year, it was reported on Tuesday that Trump has been discussing with House majority leader Kevin McCarthy a partial retreat from the terms of the bill.

Trump spent much of the past Easter weekend at his Mar-a-Lago resort in Florida, having meals with his family, watching cable news shows and rubbing elbows with conservative commentators including the Fox News host Sean Hannity. Staffers with Trump included policy adviser Stephen Miller, a chief architect of anti-immigration policies.

Trump has also repeated his call for the “nuclear option”, a change of Senate rules so a majority of 51 votes is needed to advance legislation instead of 60. Such a move has been dismissed by the Senate majority leader, Mitch McConnell.

So-called Dreamers, undocumented migrants who were brought to the US as children, are due to lose coverage under Deferred Action for Childhood Arrivals, or Daca, an Obama-era program Trump has tried to eliminate.

Trump’s favored solution for extending protections to Dreamers mustered only 39 votes in the Senate.

One new measure the administration is pursuing would end safeguards that prevent the immediate deportation of children arrested at the border alone. Under current law, unaccompanied children from countries that do not border the US are turned over to the Department of Health and Human Services and undergo often lengthy deportation proceedings before an immigration judge.

The administration is also pushing Congress to terminate a 1997 court settlement that requires the government to release children from custody to parents, adult relatives or other caretakers as their cases proceed. Many do not return to court.

The proposals appear the same as those on an immigration wishlist the White House released in October. They are likely to face opposition from Democrats and moderate Republicans, going into the midterm elections.