The homeland security secretary, Kirstjen Nielsen, defended the militarization of the US border on Friday, the morning after Donald Trump delivered an inflammatory, often factually incorrect, speech on immigration.

At a meeting hosted by the Council on Foreign Relations in New York, Nielsen was asked repeatedly about how her immigration enforcement agencies would carry out the potentially unconstitutional plans Trump outlined without detail, including a suggestion that soldiers would fire at people throwing rocks near the US-Mexico border.

Her responses, while more articulate than the president’s, perpetuated the administration’s fear-mongering narrative about immigration and specifically targeted the caravan heading to the border from Honduras that has become a political pawn ahead of the midterm elections.

“The challenge with the caravan is it’s a very amorphous concept, you don’t get a ticket to the caravan, it’s not a membership program,” Nielsen said.

The caravan has traveled 1,000km (621 miles) from San Pedro Sula in Honduras and has shrunk from 7,000 people to 4,000 halfway through its journey to the border.

Travelers, many of whom are families seeking safety by traveling in a group instead of making the trek alone, complain of illness, sunburn and exhaustion.

Previous caravans traveling from Central America have dwindled from thousands to hundreds of people by the time they reach the border. And the majority of people in them apply for asylum.

To explain why the government might send 15,000 troops to the border, instead of relying on existing homeland security department resources, Nielsen said if the caravan members took trains or buses, they could be at the border in days – and if they continued on foot, it could be at least a month until they arrive. “No, we do not have the capacity, capability to address that type of flow,” she said.

When asked whether she agreed with the president’s claim that an “invasion” was coming north, Nielsen described “second and third” waves of people migrating to Mexico, claiming they have been violent. “By the time we’re talking about molotov cocktails and use of firearms, it’s my duty to make sure our officers and agents are secure,” she said.

There is a second group of 300 people from El Salvador and a third group that confronted police at the Guatemala-Mexico border on Sunday. Some threw rocks and glass bottles and local first responders told Reuters that 26-year-old Henry Adalid was killed by a rubber bullet. The Mexican government denied that officers were armed.

“In general, mass migrations are dangerous for the migrants themselves,” Nielsen said. “It needs to be safe, it needs to be orderly.”

Nielsen’s defense of increased border militarization comes amid two years of efforts by the Trump administration to restrict immigration to the US, including by targeting the asylum and refugee process.

In June, the attorney general, Jeff Sessions, ordered US immigration courts to stop granting asylum to victims of domestic abuse and gang violence.

In August 2017, the Trump administration announced it shut down the Central American Minors (Cam) program, which allowed people lawfully in the US to apply for refugee resettlement or temporary immigration status for their children or other eligible family members.

It has also shrunk refugee admissions to a record low – making it more difficult for people to apply for refuge from their home country instead of pursuing a case at the border.

Though Nielsen met on Friday morning to discuss election security, the crowd of consultants, professors and not-for-profit workers questioned her instead on the administration’s immigration policies for nearly all of the 30 minutes allotted for a question and answer period.

There were also protesters gathered outside each entrance to the Upper East Side building, carrying signs calling for the release of asylum seekers and showing closeup images of the ankle monitors used to track detained migrants waiting to face immigration court.

One guest questioned Nielsen on Trump’s family separation policy, which allowed for mass separations of migrant children from their parents before Trump ended the policy amid public outcry.

“What were you thinking when you announced that policy without having a tracking system?” asked Nina Gardner, a lecturer at Georgetown University.

Gardner said luggage was treated with more respect than separated immigrant families, and asked: “What are we doing to reunify the children with their families now and how do you stay up at night?”

Nielsen laughed before responding. “Thank you for the way in which your question was asked,” she said before mischaracterizing the family separation process.

“I could say that DHS reinforced the law and unfortunately some parents chose to break the law and enter the country in the way that did not go to a port of entry,” Nielsen continued. “We do have a tracking system.”

Hundreds of families had been separated before the zero tolerance policy that allowed for family separation was announced in April and previous administrations only separated families if the adult posed a demonstrable risk to the child.

The tracking system that exists now is the result of a lawsuit brought by the American Civil Liberties Union on behalf of more than 2600 separated children demanding reunification of families.

The DHS watchdog, the office of inspector general (OIG), said last month that the agency separated families without a system in place. The OIG report said: “DHS was not fully prepared to implement the administration’s zero tolerance policy or to deal with some of its after-effects.”