The US president added that the visa program to bring in the best of the worldwide workforce "should include only the most skilled and highest-paid applicants and should never ever be used to replace American workers".
"The buy-and-hire American order I'm about to sign will protect workers and students like you", Trump said.
The H-1B visa program paves the way for the majority of highly-skilled workers from other countries to work in the U.S. The visas are doled out through a lottery system, and there are usually about three times as many applicants as there are visas.
In yesterday's White House briefing, one of the unnamed agency executives called out three of these firms, saying, "The top recipients of the H-1B visa are companies like Tata, Infosys, Cognizant".
The Indian government, on its part, has said it will take up the issue with the American authorities during the upcoming visit of Finance Minister Arun Jaitley to the US.
"The idea that Donald Trump is dramatically turning his back on his "America first" policy as well as his comment that the dollar is "too strong" are hurting the U.S. currency", Lawler said.
Last year, Disney was accused of taking advantage of the H-1B visa scheme to lay off American technology workers, who were forced to train their foreign replacements.
Trump's order seeks to ensure the visas go only to the most skilled workers. "The reality of it is that employers are not required to recruit and try to hire USA workers before they hire an H-1B worker".
Government data released this week, meanwhile, shows that the number of applicants for H-1B visas has fallen. Trump has turned over management of his business empire to his two adult sons, Donald Jr. and Eric, and says he will have no contact with them about their business decisions.
The tech industry has argued that the H-1B program is needed because it encourages students to stay in the US after getting degrees in high-tech specialties and companies can't always find enough American workers with the skills they need.
The Reuters news agency examined U.S. Labor Department records and found that more than 15 percent of Facebook's employees in the United States in 2016 used a temporary work visa. "Measures to protect American workers will not be successful if they are applied selectively".
"Buy American" provisions also may run afoul of free trade agreements, though the White House wants to conduct a full review before seeking adjustments to those trade agreements.