WASHINGTON — The White House unsuccessfully tried to pressure the Homeland Security Department to end a program that allows hundreds of thousands of people from countries affected by natural disasters or violence to live in the United States without fear of being deported, according to people familiar with the discussions.

John F. Kelly, the White House chief of staff, made an 11th-hour plea to Elaine Duke, the acting Homeland Security secretary, ahead of a deadline this past Monday to decide about the status of immigrants in the program from Honduras and Nicaragua.

Ms. Duke ultimately delayed for six months a decision on the status of immigrants from Honduras, saying she had concluded after an internal department review that she did not have enough information about conditions in the country to decide. But she ended the protected status for thousands of immigrants from Nicaragua who came to the United States illegally after Hurricane Mitch in 1998.

Accounts of her phone calls with Mr. Kelly laid bare the strains between Trump administration officials trying to reduce both legal and illegal immigration — a campaign promise of President Trump’s — and career immigration officials who see those efforts as overly broad and harsh.