The president's "Buy American, Hire American" executive order has sought to reform programs like the H-1B visa scheme.
"As of May 21, 2018, the USCIS has received over 5,000 tips to the dedicated H-1B email address," USCIS spokesperson Philip Smith said.
The lawsuit claims that USCIS with its new policy memo overstepped its role in overseeing the H-1B visa program.
U.S. Citizenship and Immigration Services said the temporary suspension will allow it to process petitions that have been pending for a long time.
Immigration experts have questioned how Melania Trump gained permanent legal residency.
Restrictions have led many H-1B visa holders in the U.S. to move or contemplate moving north to Canada.
"The H-1B visa is over," said Vikram Rangnekar, who founded MovNorth.com, a platform dedicated to helping highly skilled foreign workers make the move from the U.S. to Canada.
Two proposals that would have provided Dreamers with a pathway to citizenship and provided funding for Trump's border wall failed.
Silicon Valley relies on more foreign-born workers than domestic ones, reports say.
Senator Chuck Grassley made his comments during a congressional hearing on homeland security on Tuesday.
President Donald Trump's administration has publicly said its looking to curb H-1B visa extensions, but it has also quietly been bogging current visa holders down in new paperwork.
U.S. Citizenship and Immigration Services has said it is "not considering a regulatory change that would force H-1B visa holders to leave the United States."
"Mr. President, would America really be greater without us?" Democratic Congressman Ro Khanna, whose parents are Punjabi and immigrated to the U.S. from India, asked.