Mr Trump tried to make capital out of Monday night’s search of his Mar-a-Lago home, citing the apparent investigation into his handling of classified material in text messages and emails soliciting political donations from his supporters.
“There is no mountain we cannot climb, there is no summit we cannot reach, there is no challenge we cannot meet,” Mr Trump said in the new video, which included an extended critique of the Democratic Biden administration. “We will not bend, we will not break, we will not yield.”
The advert was followed by fundraising appeals highlighting the raid.
Allies of Mr Trump are demanding an explanation for the search.
Sources are reported to have said the raid - the first involving a former US president’s home - was approved at the highest levels of the Department of Justice, although there has been no official comment.
US Senate Republican Leader Mitch McConnell said the country deserved a “thorough and immediate explanation” of what led to the search.
Mr Trump’s former Vice-President Mike Pence called on the attorney general to give “a full accounting” of why the search warrant was carried out.
“No former President of the United States has ever been subject to a raid of their personal residence in American history,” he wrote on Twitter.
Some Republicans in Congress have vowed to launch an investigation of the search itself if they recapture control of the House or Senate in November’s midterm elections.
Mr Trump has been flirting publicly with the question of running again for president in 2024 but has not said clearly whether he will do so.
Meanwhile the former president indicated he would testify on Wednesday in a New York investigation by the state’s attorney general into his family’s business practices.
New York State Attorney General Letitia James is conducting a civil investigation examining whether the Trump Organization inflated real estate values.
Mr Trump has denied wrongdoing and called the New York investigation politically motivated.