Trump's latest Twitter salvo followed a report in the Washington Post that the president and his advisers have discussed replacing Sessions, one of the Republican billionaire's earliest supporters.
"Attorney General Jeff Sessions has taken a VERY weak position on Hillary Clinton crimes (where are E-mails &DNC server) & Intel leakers!" Trump tweeted.
Trump has openly criticized Sessions for recusing himself from overseeing a federal probe into possible collusion between the Trump campaign and Russia to meddle in the 2016 US presidential elections.
Sessions has said he has no plans to resign.
With pressure mounting from the investigation led by former FBI director Robert Mueller, Trump has sought to revive an election year controversy over Clinton's use of a private server to send email while secretary of state.
The White House also alleged last week that the Democrats colluded with Ukraine during the 2016 campaign, adding another twist to the president's counter-offensive.
"Ukrainian efforts to sabotage Trump campaign - 'quietly working to boost Clinton.' So where is the investigation A.G.," Trump said in another early morning tweet Tuesday.
- 'Beleaguered' -
US presidents normally go to great pains to avoid being seen as influencing ongoing or possible investigations, making Trump's attacks on Sessions all the more extraordinary.
On Monday, Trump took to Twitter to declare his top law enforcement official "beleaguered" as he wondered out loud why Sessions was not investigating Clinton.
"So why aren't the Committees and investigators, and of course our beleaguered A.G., looking into Crooked Hillarys crimes & Russia relations?" Trump asked.
Trump has expressed increasing anger with Sessions as his Justice Department's investigations into possible Trump-Russia collusion has quickened.
Last week, he publicly upbraided Sessions for stepping back from issues related to the probe.
Sessions recused himself because of his role on Trump's campaign and because he failed to tell the Senate during his confirmation hearings about contacts he had with the Russian ambassador in Washington.
Trump said he would never have hired Sessions had he known he would recuse himself.
"I think is very unfair to the president," Trump told The New York Times last week. "It's extremely unfair, and that's a mild word, to the president."
- Widening probe -
Trump's eldest son, son-in-law and top aides have become entangled in the widening investigation led by Mueller.
Jared Kushner, the president's son-in-law and a top White House official, was questioned Monday by a Senate panel about contacts with then Russian ambassador Sergey Kislyak, a Russian financier and a Russian lawyer who offered dirt on Clinton.
Kushner made a statement denying collusion after testifying behind closed doors, insisting the string of undisclosed meetings with Russian officials were "proper."
"Jared Kushner did very well yesterday in proving he did not collude with the Russians. Witch Hunt. Next up, 11 year old Barron Trump!" Trump tweeted on Tuesday.
In May, Trump fired FBI director James Comey over the bureau's investigation into Russia.
That led to Mueller's appointment as a special prosecutor.
The Post report said Trump associates see getting rid of Sessions as part of a potential strategy to fire Mueller and end the Russia investigation.
The website Axios reported that Trump was considering replacing Sessions with another early supporter, Rudy Giuliani, a former New York mayor.
But Giuliani dismissed the report and said Sessions was right to have recused himself from the Russia probe, CNN reported.
Sessions "made the right decision under the rules of the Justice Department," CNN quoted Giuliani as saying as he arrived at Ronald Reagan Washington National Airport.
