"I greatly appreciate Nancy Pelosi’s statement against impeachment, but everyone must remember the minor fact that I never did anything wrong, the Economy and Unemployment are the best ever, Military and Vets are great - and many other successes!" the president tweeted.
"How do you impeach a man who is considered by many to be the President with the most successful first two years in history, especially when he has done nothing wrong and impeachment is for 'high crimes and misdemeanors'?"
Mr Trump's outburst came after House speaker Ms Pelosi said she did not support the pursuit among some in her party of the president's impeachment.
“I’m not for impeachment. This is news. I’m going to give you some news right now because I haven’t said this to any press person before," she told the Washington Post Magazine on Monday.
“But since you asked, and I’ve been thinking about this: Impeachment is so divisive to the country that unless there’s something so compelling and overwhelming and bipartisan, I don’t think we should go down that path, because it divides the country. And he’s just not worth it.”
Mr Trump followed up his claims of innocence with an attack on late night comedy shows, many of which he accuses of unfairly targeting him.
“Jay Leno points out that comedy (on the very boring late night shows) is totally one-sided. It’s tough when there’s only one topic," Mr Trump wrote, quoting something apparently said on his favourite Fox News show, Fox & Friends.
He added: "Actually, the one-sided hatred on these shows is incredible and for me, unwatchable. But remember, WE are number one - President!"
Mr Trump continued with a pair of tweets sent within a minute of each other. The first read, "MAKE AMERICA GREAT AGAIN!" and the second, "KEEP AMERICA GREAT!"
Addressing California's move this week to suspend all further executions, Mr Trump next launched an attack on the state's Democratic governor, Gavin Newsom.
"Defying voters, the Governor of California will halt all death penalty executions of 737 stone cold killers," he tweeted. "Friends and families of the always forgotten VICTIMS are not thrilled, and neither am I!"
Despite Mr Trump's claim hundreds of murderers would now dodge justice, there have been no executions in the state since 2006 following a court-ordered moratorium on the death penalty, which ruled its lethal injection protocol was unconstitutional.
A new execution protocol was under review, but Mr Newsom's order will now withdraw it.
Mr Trump concluded his string of tweets with an attack on the Justice Department, which is currently investigating the president and his campaign over potential links to Russia.
"The just revealed FBI Agent Lisa Page transcripts make the Obama Justice Department look exactly like it was, a broken and corrupt machine," he tweeted. "Hopefully, justice will finally be served. Much more to come!"
The president was referring to newly released transcripts from congressional testimony last year by former FBI lawyer Lisa Page, who has been accused by Republicans of anti-Trump bias.
She told lawmakers in a closed-door interview about 2016 texts between her and former FBI agent Peter Strzok, in which they discussed a so-called "insurance policy" involving Mr Trump before he became president.
Ms Page said it was a reference to the fact the FBI's then-counterintelligence probe into whether a Trump campaign official was colluding with Russia would become much more significant if he won the election.
Mr Trump's tweeting on Wednesday morning started just 6 hours and 27 minutes after his final tweet the previous evening, in which he hailed the growing US economy as a "beautiful thing to watch".