WASHINGTON—President Trump’s top disaster official cost the government $151,000 through the unauthorized use of government vehicles that included travel to his home in North Carolina, according to an internal investigation.

Brock Long, the head of the Federal Emergency Management Agency, also relied on government vehicles and employees to drive him and his family around Hawaii during a trip that included official functions and a vacation, according to the Department of Homeland Security’s inspector general.

Mr. Long’s use of government vehicles and staff cost $94,000 in salary, $55,000 in travel expenditures and $2,000 in maintenance-related costs, according to a portion of the inspector general’s report obtained by The Wall Street Journal.

Kirstjen Nielsen, the DHS secretary, released a statement Friday night saying that she had ordered Mr. Long to repay the government “as appropriate.” A spokesman for Ms. Nielsen said Tuesday that the secretary and Mr. Long hadn’t yet agreed on the total that would be repaid.

In the same statement on Friday, Mr. Long said he would “accept full responsibility for any mistakes that were made by me.” He didn’t specify what those mistakes were. A spokeswoman declined to comment Tuesday.