There are legitimate reasons someone might be targeted, such as evidence of a connection to terrorism or crime. But advocates also said they worry about people being profiled for extra scrutiny because of their name or nationality.

“This will certainly slow down the screening process and impose a substantial burden on these applicants,” said Greg Chen, the director of advocacy for the American Immigration Lawyers Association. “It will make it much harder and create substantial delays.”

The cables from Mr. Tillerson, which were reported by Reuters, make clear that the Trump administration wants a more intense focus on the potential for a serious threat when making decisions about who should receive a visa.

“Consular officers should not hesitate to refuse any case presenting security concerns,” Mr. Tillerson wrote in the cables, titled “Implementing Immediate Heightened Screening and Vetting of Visa Applications.”

“All visa decisions are national security decisions,” the secretary of state added.

During his presidential campaign, Mr. Trump accused the Obama administration of failing to properly screen people coming into the United States, a claim former officials in that administration reject. As a candidate, Mr. Trump vowed to ban all incoming Muslims until leaders could “figure out what the hell is going on.” Later, he backed away from a total ban on Muslims but promised “extreme vetting” of those trying to come to the United States.

The president’s first attempt to put tougher screening in place was the executive order aimed at temporarily blocking refugees and people whom Mr. Trump called “bad dudes” from predominantly Muslim countries. Courts blocked the first version of the president’s order after a chaotic rollout just days into his term. A second order was blocked this month.

But on March 6, the same day that Mr. Trump issued his revised travel ban, he also wrote a presidential memorandum ordering the secretary of state, the attorney general and the secretary of homeland security to “implement protocols and procedures” to enhance visa screening.