President Obama’s convention speech on Wednesday has triggered Mr Trump to post a series of angry tweets. Mr Trump furiously wrote: “HE SPIED ON MY CAMPAIGN, AND GOT CAUGHT!”
His tweet references what he calls “Obamagate” which criticises the FBI and investigators who examined his campaign for Russian ties in 2016.
Speaking in Philadelphia, Mr Obama said Mr Trump had “no interest in putting in the work”.
He said: “This administration has shown it will tear our democracy down if that’s what it takes to win.”
Mr Trump tweeted comments about Mr Obama’s endorsement of the Democratic nominee Joe Biden, calling him “slow Joe”.
He posted: “WHY DID HE REFUSE TO ENDORSE SLOW JOE UNTIL IT WAS ALL OVER, AND EVEN THEN WAS VERY LATE? WHY DID HE TRY TO GET HIM NOT TO RUN?”
Mr Biden responded to Mr Trump’s tweets by quoting Mr Obama’s speech.
He wrote: “Donald Trump hasn’t grown into the job because he can’t.”
But the Republican senator, Lindsey Graham, backed Mr Trump by calling the Obama-Biden years “pathetically weak”.
READ MORE: Barack Obama slams Trump for treating US presidency as ‘reality show’
Mr Obama told Americans that the only way the US can restore the country was to elect Mr Biden and Ms Harris in November.
He said: “We have to get busy building it up – by pouring all our effort into these 76 days, and by voting like never before – for Joe and Kamala, and candidates up and down the ticket, so that we leave no doubt about what this country we love stands for – today and for all our days to come.”
The former president’s comment were the harshest criticisms he has made against Mr Trump to date.
Previously, Mr Obama has followed presidential traditions of holding back from criticizing a successor.
Mr Obama said: “I have sat in the Oval Office with both of the men who are running for president.
“I did hope, for the sake of our country, that Donald Trump might show some interest in taking the job seriously; that he might come to feel the weight of the office and discover some reverence for the democracy that had been placed in his care.”