WASHINGTON—Former President Donald Trump’s efforts to claim absolute immunity to ward off criminal and civil legal actions against him were rebuffed twice Friday in separate legal decisions.

U.S. District Judge Tanya Chutkan, presiding over Trump’s election-interference case brought by special counsel Jack Smith, rejected the former president’s bid to have that case tossed out on the grounds that he enjoys “absolute immunity” from criminal prosecution. In court papers, the former president’s lawyers argued that his efforts to challenge his November 2020 election loss had been “within the ‘outer perimeter’ of his official responsibility” as president.