Trump's latest Twitter salvo followed a report in the Washington Post that the president and his advisers have discussed replacing Sessions, once one of his closest allies.
"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 Russian 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 a campaign year controversy over Clinton's use of a private server to send email while secretary of state.
During the campaign, former FBI director James Comey, whom Trump later fired over the Russia probe, had declined to recommend Clinton be prosecuted over her handling of classified material on her email server.