"At the request of Democrats, I have delayed the Illegal Immigration Removal Process (Deportation) for two weeks to see if the Democrats and Republicans can get together and work out a solution to the Asylum and Loophole problems at the Southern Border," Trump tweeted on Saturday.
"If not, deportations start," he added.
Media reports said on Friday that the Trump administration is expected to kick off pre-dawn raids on Sunday on up to 2,000 migrant families facing deportation orders in 10 cities including Los Angeles, Houston, Chicago, Miami, New York and San Francisco, based on cases filed in 10 immigration court locations, reports Xinhua news agency.
The imminent operation raised concerns about more family separations. Both Chicago and Los Angeles mayors said their cities would not assist in the raids.
"We are all aware of the threat from President Trump regarding raids by ICE, and in response, Chicago has taken concrete steps to support our immigrant communities," Chicago Mayor Lori Lightfoot tweeted on Friday. "CPD (Chicago Police Department) will not cooperate with or facilitate any ICE enforcement actions."
Los Angeles Mayor Eric Garcetti also said in a statement: "Los Angeles will always stand with our immigrant brothers and sisters, and our law enforcement officers will never participate in these actions."
Trump defended the plan on Saturday morning, saying in a tweet: "The people that ICE will apprehend have already been ordered to be deported. This means that they have run from the law and run from the courts."
In February, the Immigration and Customs Enforcement (ICE) sent some 2,000 letters to families who already had received final orders of removal by judges in absentia, asking them to self-report to local ICE offices by March to comply with the orders.
The upcoming operation is expected to target them.
However, acting Homeland Security Secretary Kevin McAleenan has reportedly been urging ICE to take a more limited approach to detain a group of about 150 families who had attorneys but dropped out of the legal process and absconded, warning that the widespread operation could risk separating children from their parents.
Once arrests take place, families will likely be moved to ICE residential detention centres as the agency works with consulates to obtain travel documents.
( With inputs from IANS )