Trump, who defeated Democrat Hillary Clinton in last year's presidential election but continues to use her as a foil, questioned why his attorney general, Jeff Sessions, and special counsel Robert Mueller were not investigating former FBI Director James Comey or Clinton, for her email practices as secretary of state.
"So many people are asking why isn't the A.G. or Special Counsel looking at the many Hillary Clinton or Comey crimes. 33,000 emails deleted...," he wrote on Twitter.
"My son Donald openly gave his e-mails to the media & the authorities whereas Crooked Hillary Clinton deleted (& acid washed) her 33,000 e-mails!"
The Federal Bureau of Investigation decided last year not to recommend criminal charges against Clinton for her email practices. Trump fired Comey in May.
Sessions had been Trump's first supporter in the Senate before being named attorney general, but recently has become a lightning rod for Trump's anger over the probe into allegations of Russia's meddling in the 2016 presidential election. Sessions recused himself from the probe in March after having failed to disclose at his confirmation hearing that he had held meetings last year with Russia's ambassador.
The U.S. Senate Judiciary Committee said on Friday that Trump's eldest son, Donald Trump Jr., and Trump's former campaign manager Paul Manafort had agreed to negotiate whether to be interviewed by the panel in its Russia investigation.
The Washington Post reported on Thursday that Trump had inquired about his authority to issue pardons to aides, family members and perhaps himself as Mueller’s Russia probe widens.
Trump cited his power to pardon in the series of tweets on Saturday that focused ire on leaks to the news media.
"While all agree the U.S. President has the complete power to pardon, why think of that when only crime so far is LEAKS against us. FAKE NEWS," he wrote.
Scholars have raised questions about the scope of the president's legal authority in issuing pardons. If sometime in the future Trump moved to pardon himself, the U.S. Supreme Court might have to decide on the constitutionality, some have speculated.
Trump also had words for Republican senators who have not been able to agree on a way forward to repeal and replace former President Barack Obama's healthcare law, the Affordable Care Act, which has become known as Obamacare and which Trump promised to do away with as president.
"The Republican Senators must step up to the plate and, after 7 years, vote to Repeal and Replace. Next, Tax Reform and Infrastructure. WIN!" he tweeted.
Trump left on Saturday morning for a short trip to Norfolk, Virginia, where he will be present for the commissioning ceremony for an aircraft carrier, the Gerald R. Ford, named after the former U.S. president.
Ford, who became president after Richard Nixon resigned, in 1974 pardoned Nixon for any crimes he might have committed stemming from the Watergate scandal that led to his resignation.