By Agence France-Presse
Among the affected websites was one belonging to Ohio Governor John Kasich.
Posted on the websites was a message, from a group calling itself Team System DZ, vowing revenge against US President Donald Trump.
"You will be held accountable Trump, you and all your people for every drop of blood flowing in Muslim countries," it read, adding: "I Love Islamic state."
The messages, written in gold lettering against a black backdrop, also displayed a white symbol with what looked like Arabic script.
The one posted on Kasich's website also played an Islamic call to prayer.
A website for Howard County, Maryland, several miles outside Washington DC, was also affected.
Some of the websites remained out of service early Monday, while Kasich's www.governor.ohio.gov site was back up and running after being taken offline Sunday.