“Due to the military coup and security forces’ brutal violence against civilians, the people of Burma are suffering a complex and deteriorating humanitarian crisis in many parts of the country,” Homeland Security Secretary Alejandro Mayorkas said in a statement Friday.

The Department of Homeland Security didn’t respond to a question about how many Burmese people could benefit from the new status.

Myanmar’s military seized control of the government Feb. 1, detaining civilian leader Aung San Suu Kyi and senior members of her National League for Democracy party.

Since then a protest movement has erupted, and the military has used violence to put down dissent, leaving dozens of people dead in crackdowns.

Authorities have rounded up hundreds of protesters, politicians and activists from the streets and in nightly raids on their homes. A politician arrested Saturday night was confirmed dead in a military hospital the next morning, his party said.

DHS said that the status afforded to citizens of Myanmar doesn’t give a green light to new immigration and that “for their own health and safety, individuals should not believe smugglers or others claiming the border is now open.”

The U.S. has imposed several rounds of sanctions on the military leaders and people connected with them. On Wednesday, the Treasury Department announced sanctions on the adult children of the military leader Min Aung Hlaing, including a restaurant and gallery owned by one of the children in Yangon, also known as Rangoon.

“We reiterate our calls to the military and the police to stop the violence and arbitrary detentions, to release all those unjustly detained, and again, to restore the democratically elected civilian government of Burma,” State Department spokesman Ned Price said Friday.

The United National Security Council, which this month is led by the U.S., unanimously condemned Wednesday the violence against protesters in Myanmar.

The Security Council is also looking to address “shared concerns about how the violence might worsen the plight of internally displaced persons in Burma and Rohingya refugees, and exacerbate existing challenges,” said Linda Thomas-Greenfield, the U.S. ambassador to the U.N. A military operation forced more than 740,000 members of the Rohingya Muslim minority out of the country in 2017.

On Monday, the Biden administration granted temporary protection status to Venezuelans living in the U.S. illegally. The decision was expected to affect as many as 320,000 Venezuelans in the U.S.

Write to William Mauldin at william.mauldin@wsj.com