In 1981, Israel effectively annexed the areas of the Golan it had captured 14 years earlier through the Golan Heights Law, which extended Israeli "laws, jurisdiction and administration" to the area.
Israeli sovereignty over the Golan has not been internationally recognised.
Mr Katz's comments come after the US moved its embassy from Tel Aviv to Jerusalem. He said America recognising Israeli sovereignty over Golan would be a clear signal to Iran.
“This is the perfect time to make such a move,” he said.
“The most painful response you can give the Iranians is to recognise Israel’s Golan sovereignty - with an American statement, a presidential proclamation, enshrined (in law).”
As recently as March 2017, the United Nations Human Rights Council (UNHRC) condemned what it described as Israel’s “occupation” of the Golan Heights.
At the time, UK Foreign Secretary Boris Johnson described the UNHRC’s criticism as “absolutely preposterous”, especially “when after all in that region of Syria we have seen the most appalling barbarity by the Assad regime.”