(CNN) Homeland Security Secretary John Kelly said Friday night the United States has not been "rounding anyone up," after immigration authorities acknowledged arrests of undocumented migrants across the country this week.

"They're not rounding anyone up," Kelly said at the San Ysidro Port of Entry between San Diego and Tijuana. "The people that ICE (Immigration and Customs Enforcement) apprehend are people who are illegal, and then some."

Kelly said he went on two "knock and talk" visits to homes before 6 a.m. Friday, during which authorities apparently took into custody three people, including "a particularly bad individual."

Kelly's comments followed growing fear and confusion for some immigrants and their families and advocates.

Earlier Friday, Mexico warned its citizens living in the United States to "take precautions" and remain in contact with consular officials, following the deportation of an undocumented mother while she was on a routine check-in with US immigration authorities.

The fears and warnings come amid court battles over President Donald Trump's proposed ban on immigrants from seven majority-Muslim nations. Trump has also vowed to deport some 3 million undocumented immigrants who have criminal records.

He has famously promised to build a wall at the US-Mexico border to block illegal immigration.

Guadalupe Garcia de Rayos, 35, was deported Thursday after she checked in with the US Immigration and Customs Enforcement office in Phoenix a day earlier.

The action sparked protests by the mother's supporters and drew praise from proponents of stricter enforcement of immigration laws.

ICE said most of the people targeted this week -- in homes and workplaces from Southern California to Atlanta and other cities -- are criminals.

Arrests and fear

In Los Angeles, ICE said Friday that it had arrested about 160 people from a dozen countries during a five-day, five-county operation aimed at undocumented criminals, immigration fugitives and people who re-entered the United States illegally after deportation.

About 150 of the suspects have criminal histories, including felony convictions for serious or violent offenses, according to an ICE statement. There were 10 people with no criminal history but five had orders of removal or had been previously deported.

The ICE statement said the arrests were part of what it called a regular "enforcement surge." It denied reports about ICE checkpoints and random sweeps, calling them "false, dangerous, and irresponsible."

"These reports create panic and put communities and law enforcement personnel in unnecessary danger," the statement said.

Los Angeles Mayor Eric Garcetti issued a statement Friday night asking ICE for "greater transparency about ongoing operations" within the city.

ACLU Texas Executive Director Terri Burke told CNN that "raids" had been happening in Austin "the last few nights."

"It is not unlike some of the things Obama did, but it's ramped up and worse," Burke said.

Roger Rocha, the national president of the League of United Latin American Citizens, said, "It appears that ICE has started its effort to make good on campaign promises regarding mass deportations of undocumented individuals whose only crime is a lack of status."

In the Texas capital, City Councilman Greg Casar said children in Austin "have not come to school" and "families ... have locked themselves into their apartments" because of ICE enforcement actions, according to CNN affiliate KEYE-TV

Arizona mother deported to Mexico

"The case involving Mrs. Garcia de Rayos illustrates a new reality for the Mexican community living in the United States, facing the most severe implementation of immigration control measures," Mexico's Foreign Ministry said in a statement Friday.

Mexican consulates "have intensified their work of protecting fellow nationals, foreseeing more severe immigration measures to be implemented by the authorities of this country, and possible violations to constitutional precepts during such operations and problems with due process," the statement said.

On Wednesday, Garcia de Rayos went for her routine check-in with immigration authorities, her eighth visit since her 2008 arrest and conviction for using a fake Social Security number.

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After each previous meeting, the married mother of two was released and went back to her family, but this week she was detained and deported within 24 hours to her native Mexico. Her attorney said the deportation was a direct result of President Donald Trump's crackdown on illegal immigration.

US immigration officials said there was nothing special about her case -- she committed a crime and her deportation order was enforced.

The Mexican Foreign Ministry statement said, "It is important that fellow nationals familiarize themselves with the different scenarios they might encounter and know where they can go to receive new information and know all their rights."

The statement said consular officials from Nogales, Arizona, were present when Garcia de Rayos was deported to Mexico on Thursday to ensure it was done in a "dignified and safe" manner.

Immigrants urged to 'know the risks'

Activists have said some unauthorized immigrants, fearing deportation, may skip routine check-ins with US immigration authorities.

Activists and Garcia de Rayos' attorney said they warned her she could be deported under Trump's policy. They offered sanctuary at a church, but she decided to check in with immigration authorities anyway.

In an interview Friday, Garcia de Rayos' husband, who asked that his name not be used, told CNN that unauthorized immigrants need to know the risk they face when reporting to ICE.

"They have the choice of showing up and take a chance, take a risk of being detained just like my wife was detained and deported," he said. "They also have the option of sanctuary. Or they have the option of not showing up. ... I would tell them to look for a lawyer, to look for a human rights organization."

The term "sanctuary city" is a broad term applied to jurisdictions that have policies in place designed to limit cooperation with or involvement in federal immigration enforcement actions. Cities, counties and some states have a range of informal policies as well as laws that qualify as "sanctuary" positions.

Most of the policies revolve around not cooperating with federal law enforcement on immigration policies. Many of the largest cities in the country have forms of such policies.

Number of Mexican immigrants declining

There are about 11 million unauthorized immigrants in the United States, according to the Pew Research Center.

Mexicans made up 52% of all unauthorized immigrants in 2014 , but their numbers have declined in recent years, the center reported.

The center estimates 5.8 million unauthorized immigrants from Mexico were living in the United States in 2014, down from 6.4 million in 2009.