As of early Sunday evening, there weren't any confirmed reports of migrants being apprehended in Baltimore, Chicago or New York, immigrant advocacy groups in those cities told CNN.
"For the most part, it's quiet," Cara Yi, a spokeswoman for the Illinois Coalition for Immigrant and Refugee Rights said. "We've been dispatching rapid response teams out to meet with people who have reported ICE activity over our hotline. None have been confirmed as of yet."
Most of the reports were about sightings of government vehicles, Yi said, but advocates had confirmed they were not ICE.
Acting US Citizenship and Immigration Services director Ken Cuccinelli took issue with referring to the targets of the raids as undocumented.
"They're not undocumented. They've got a court order on a piece of paper -- federal order -- that says they've gotten due process, and (there are) over a million people with removal orders. That's the pool that ICE is drawing from," he told CNN.
ICE will not comment on operational details of the raids, Cuccinelli said, adding that the priority will be apprehending violent criminals and aggravated felons. ICE agents are not "utilizing" allegations of crossing the border illegally, a misdemeanor, as cause for arrest in the raids, he said.
Asked if children would be separated from their parents, Cuccinelli said that information constituted an operational detail. But he did say families are among the 1 million people facing removal orders.
In some cities, local governments and advocacy groups were assisting the immigrants. Supporters in the Chicago neighborhood of Pilsen were posting "know your rights" fliers and encouraging residents to post the fliers, which say, "The family that resides in this home knows their legal rights," at their homes.
Advocates with the Georgia Latino Alliance for Human Rights in Atlanta on Sunday were at a popular Latino shopping center, handing out fliers that read, "ICE free zone."
The fliers also asked immigration authorities to present a signed warrant if they wanted to come inside, adding "This is OUR Constitutional Right!"
In New York City, staff members with the mayor's office of immigrant affairs are also informing immigrants of their legal rights and of city resources that are available in the event they encounter an immigration enforcement official.
"In the face of heartless raids that would tear families apart, we remain steadfast in our commitment to support and defend immigrant communities," Bitta Mostofi, the office's commissioner, said in a statement.
Cuccinelli characterized the raids as normal ICE business and pointed to statistics showing ICE has deported fewer people under President Donald Trump than it did under President Barack Obama.
"This is their job every day. We've got compassionate, loyal ICE agents who are just doing their job," he said. "It shows you how far we've fallen in that it's become news that they would actually go deport people who have removal orders."
Mark Morgan, acting commissioner for US Customs and Border Protection who was acting ICE director at the time, said the raids were postponed because operations details had been leaked. Former acting ICE director John Sandweg also expressed concern.
"You never want the target to know you're coming. You want that element of surprise because it keeps you safe," he said. "From an effective perspective, that's why you don't announce these things."
While Trump has repeatedly tweeted about the impending operation, he hasn't jeopardized officer safety, Cuccinelli said, explaining that the situation in June was different than what is happening now.
"The level of detail in the information that came out publicly (last month) was way beyond these general comments the President is making," he said.
In February, ICE sent around 2,000 letters to families who already had received final orders of removal by judges in absentia, asking them to self-report to ICE offices by March. The upcoming operation is expected to target approximately 2,000 people, the senior immigration official said.
"ICE plans these things superbly," he said.
According to Immigration and Customs Enforcement statistics, 256,085 people were deported in fiscal year 2018, up from 226,119 removals in fiscal year 2017.
Correction: A previous version of this story misstated the nature of the raids. Immigration authorities are expected to begin conducting raids targeting undocumented immigrants.
CNN's Jim Acosta, Priscilla Alvarez, Devan Cole, Kevin Liptak, Catherine E. Shoichet, Taylor Romine, Rosa Flores and Jake Tapper contributed to this report.