Pompeo is on a four-day visit to Italy and held talks with Italian President Sergio Mattarella and Prime Minister Giuseppe Conte shortly after arriving in Rome.
Farmers staged a small demonstration outside Mattarella’s residence as Pompeo showed up to the meeting.
Placards read “Don’t kill Italian food” and “Mr Pompeo we are friends”.
When Pompeo later met Conte, a journalist from a satirical television show approached him and handed him a piece of authentic parmesan cheese.
“I have a present for you — an Italian present,” journalist Alice Martinelli said.
“The prime minister knows what I am talking about. This is Parmigiano Reggiano, and this is what we make best in Italy.”
A smiling Pompeo took the cheese as Conte ordered security guards to escort Martinelli from the buiding.
“Show respect when you are a guest in someone else’s house,” he said.
Earlier this year, the World Trade Organization (WTO) ruled that Airbus had received illegal government subsidies, giving the US a green light to impose punitive tariffs.
The US has drawn up a list of EU imports worth $25 billion from which it will pick targets from aircraft and aerospace parts to wine, cheese and luxury goods.
Some Italian products, including parmesan and olive oil, are in the firing line.
Italian farmers say this is unfair because Italy is not part of the Airbus consortium.
The proposed tariffs would cost the Italian food industry billions of euros.
