On Monday, Mr Trump had called his attorney general "beleaguered".
In the latest attack, the president said in a tweet on Tuesday that Mr Sessions had "taken a VERY weak position" on investigating his former opponent in the 2016 presidential election, Democratic nominee Hillary Clinton, over her use of a private email server.
Mr Trump is angry that Mr Sessions recused himself from the federal investigation into possible collusion between Mr Trump's election campaign team and Russia. The Kremlin says it did not interfere in the election, and Mr Trump has denied any collusion.
Mr Sessions' recusal means he has no oversight of Special Counsel Robert Mueller, whose wide-ranging investigation has focused on Trump aides and the president's son-in-law Jared Kushner.
Two people close to Mr Sessions said the attorney general, who was the first Republican senator to back Mr Trump's presidential campaign, has been deeply offended by the public berating from his boss, but his resolve to stay was strong.
The public attacks by a president on a member of his own cabinet and one-time close political ally have stunned many in Washington.
"In an administration where a lot of unexpected things have happened, this may be the most unexpected. This has risen to a level that we have never seen before," said Douglas Heye, a former top aide to former Republican House Majority Leader Eric Cantor.
Republican MPs sprang to Mr Sessions' defence on Tuesday, and the top Democrat in the Senate, Chuck Schumer, accused Mr Trump of trying to "bully his own attorney general out of office".
Mr Trump's public criticism of Mr Sessions began in earnest in an interview with the New York Times last week in which he said he would not have hired him had he known he would recuse himself from the Russia investigation.
He followed that with the critical tweets, and close aides - White House press secretary Sarah Sanders and newly installed White House communications director Anthony Scaramucci - have gone on television to reinforce Mr Trump's frustration with Mr Sessions.