US Customs and Border Protection Commissioner Kevin McAleenan will replace Nielsen as the acting Department of Homeland Security Secretary.
The new measures will include additional interviews of applicants' family members, and close scrutiny of potential ties to organised crime, said senior US officials.
The US president suggested that the "dirty" eatery "badly needs a paint job" and must focus more on cleaning its "filthy canopies, doors and windows".
"We're going to be signing an executive order in a little while... We've got to be keeping families together," Trump said, as he met lawmakers on the issue.
The move has left the Democrats fuming, asserting that the Pentagon didn't seek permission.
The threat is real the Homeland Security Secretary Kirstjen Nielsen told reporters at a White House news conference.
H1-B holders in the US can rest assured that changes are soon coming which will bring both simplicity and certainty to your stay, including a potential path to citizenship: Trump.
One indictment accuses Huawei of trying to steal trade secrets from T-Mobile, and of promising bonuses to employees who collected confidential information on competitors. A second indictment claims the company worked to skirt US sanctions on Iran.
"Terrorists won't win," New York Mayor Bill de Blasio said after a blast at the Port Authority terminal in Manhattan during the morning rush hour on Monday, which injured four.
