WASHINGTON — The string of insults, misstatements, exaggerations and outright falsehoods emanating from the White House began just after sunrise.

In the space of a few hours, President Trump on Tuesday took credit for averting a war with North Korea, charged without proof that President Barack Obama had secretly granted citizenship to thousands of Iranians as part of nuclear disarmament negotiations and appeared to suggest that customers of the motorcycle maker Harley-Davidson were psychic.

He called a sitting congresswoman “crazy” and “corrupt.” He branded the National Security Agency’s handling of millions of telephone call records “a disgrace” — and suggested it was connected to the special counsel investigation into whether his campaign worked with Russia to interfere in the 2016 elections.

“Witch Hunt!” he wrote at the end of that tweet.

The posts on Twitter spanned a range of foreign and domestic issues, and seemed to hew to two clear themes: Attacks on Mr. Trump’s perceived rivals, and trumpeting of what he considers his proudest achievements in the face of public criticism.