Mr Obama made stops in Pennsylvania and Florida to stump for Mr Biden.
Fox News aired coverage of one of Mr Obama's speeches, much to Mr Trump's displeasure.
The president mentions Mr Obama on a regular basis during his rallies and in interviews. Mr Trump often blames the Obama administration for leaving him "a mess" and regularly accuses Mr Obama of spying on his campaign prior to the 2016 election.
"Remember I wouldn't be President now had Obama and Biden properly done their job," Mr Trump wrote on Twitter. "The fact is, they were TERRIBLE!!!"
Mr Trump claimed that "every time [Mr Obama] speaks, people come over to our side."
Ben LaBolt, a former spokesman for Mr Obama, told The Hill that the former president was clearly getting to Mr Trump.
“He has allowed Obama to get under his skin and is obsessed with the fact that his presidency pales in comparison to the prior one,” he said. “He is living in a fantasy land where he is just a celebrated cable commentator on Fox commenting on the conspiracy theory of the day and he doesn’t have to run against Joe Biden to win another term. But reality is creeping up on him fast.”
During Mr Obama's appearance in Orlando, Florida, the former president accused Mr Trump of being jealous of Covid-19 because it gets more attention than he does.
“What’s his closing argument? That people are too focused on COVID. He said that at one of his rallies. 'COVID, COVID, COVID.' he’s complaining. He’s jealous of COVID's media coverage," Mr Obama said. "If he had been focused on COVID from the beginning, cases wouldn’t be reaching new record highs across the country this week.”
Mr Trump has tried - and has pledged to keep trying - to dismantle Mr Obama's political legacy, the Affordable Care Act.
While Mr Trump frequently boasts that he eliminate the individual mandate portion of the healthcare bill, he has yet to actually dismantle the policy.
The president has made it clear that his goal is to undermine the Obama-era policy and replace it with his own healthcare plan, though Mr Trump has yet to provide any details of how that plan.
Eddie Vale, a Democratic strategist, told The Hill that there’s “probably 100 different reasons” for why Mr Trump has taken aim at Mr Obama in recent days.
But, he said, “to get into a back and forth with a former president who is way more popular than him is both absolutely insane and perfectly captures Donald Trump.”