Donald Trump says US is removing people who have come in over the years illegally. (File)

US President Donald Trump said on Friday mass deportation roundups would begin "fairly soon" as US migrant advocates vowed their communities would be "ready" when immigration officers come.

Trump, who has made a hardline immigration stance a key issue of his presidency and his 2020 re-election bid, postponed the operation last month after the planned date was leaked to the press, but on Monday he said the roundups would take place after the July 4 holiday.

"They'll be starting fairly soon, but I don't call them raids, we're removing people, all of these people who have come in over the years illegally," he told reporters at the White House on Friday.

US Immigration and Customs Enforcement (ICE) last month said raids would target undocumented migrants who had recently arrived in the United States so as to discourage a surge of Central American families at the southwest border.

ICE did not immediately respond to a request for comment on Trump's statement.

ICE operations are expected to involve "collateral arrests" in which undocumented migrants not directly targeted by officers are picked up in raids.

Government documents published this week by migrant rights groups showed some past ICE raids had more collateral arrests than apprehensions of targeted migrants. Migrant rights groups say this general, looming threat to undocumented migrants is harmful to communities and the U.S. economy, as it forces adults to miss work and children to skip school out of fear they may be picked up and separated.

"We have to be ready, not just when Trump announces it, because there are arrests every day and they have been increasing," said Elsa Lopez, an organizer for New Mexico immigrant and workers' rights group Somos Un Pueblo Unido.

Migrant apprehensions on the southwest border hit a 13-year high in May but eased in June as Mexico increased immigration enforcement.

An increasing number of migrants are coming from countries outside Central America, including India, Cuba and Africa. The Del Rio, Texas, Border Patrol sector on Friday reported the arrest of over 1,000 Haitians since June 10.

Democratic lawmakers visited an El Paso, Texas, Border Patrol station on Monday and said migrants were being held in atrocious conditions, with women told to drink out of a toilet.

To "dispel" what he called "the misinformation," Chief Border Patrol Agent Roy Villareal put out a video showing fresh water available from a cooler and a faucet in a cell at a Tucson, Arizona, sector migrant processing centre.

"We're not forcing aliens to drink out of the toilet," said Villareal, head of an area that in May apprehended nearly six times fewer people than the El Paso sector, a stretch of border that has borne the brunt of the migrant surge.