Sunday was set to be the busiest of days for immigration officers.
According to the report, Pelosi called Trump and spoke with him for about 12 minutes, several hours before the postponement was announced.
The president had told Pelosi that he would consider the request, said the person familiar with the situation.
She called the raids "heartless".
Mrs. Pelosi, in her statement Saturday, suggested there is no cause to deport any illegal immigrant who hasn't amassed a serious criminal record.
James added that those who wish to check whether a removal order has been issued against them can call the Immigration Court's information system at 1-800-898-7180 and that those that need advice can call the Office of New Americans hotline at 1-800-566-7636.
Republican allies of Trump in Congress have proposed an overhaul of immigration law that would force migrants to claim asylum from their own country or Mexico, a plan widely derided by human rights groups and immigrant activists.
Earlier Sunday, Trump defended the raids via Twitter, arguing that the targeted families have been dodging the law.
Although ICE arrests people a variety of ways, it's the larger enforcement operations such as a workplace sting that draw the most attention. Surprise is also an important element.
'These are people that are supposed to go back to their home country. Immigrants are not required to open their doors, and increasingly they don't.
Last fiscal year, ICE's Enforcement and Removal Operations unit arrested over 158,500 individuals in the country illegally, an 11 percent increase over the prior year and the highest number since 2014. Immigrant advocates stepped up know-your-rights campaigns.
Another complication is that ICE needs travel paperwork from a home country to deport someone, so immigrants often end up detained at least temporarily waiting for a flight. "They have gone through the process, the process has rendered their decision and so those are the people that are being affected by the publicized mass raids".
I don't want to go to war with Iran
It's unclear whether Iran's national leadership approved of the strike, a fact that Trump apparently knew as well. Trump says the crowd was blessed to be gathered during "a truly exciting time in America, in American history".
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