Ofcom
The presenter was met with a huge backlash on social media over comments he made during a discussion about the war in Ukraine.
The corporation has said it "accepts" Ofcom's decision, which relates to a BBC News broadcast last month.
The presenter had questioned whether threats made against the Labour leader were "a big deal", but later clarified his remarks.
"We have told ITV that greater care should be taken by trusted medical experts when presenting facts and figures on public health issues."
The LBC presenter sparked nearly 850 complaints with his remarks about the Strictly Come Dancing star in October.
Piers' comments about Meghan Markle' led to a record number of Ofcom complaints earlier this year.
Her outburst towards boyfriend Teddy Soares sparked more Ofcom complaints than any other scene in Love Island history.
"I put that post on social media asking if I’d get my job back to prove a point."
More than 25,000 people complained to the TV watchdog after Faye's outburst towards boyfriend Teddy Soares.
She also recalled how Piers' final two days at Good Morning Britain were "very challenging" for her.