The meeting of the leaders at Rivlin's home was part of Duterte's four-day visit to Israel, where he at some point is expected to agree to buy Israeli oil and weapons.
Duterte praised Israel for selling arms to the Philippines, which he said are helping defeat terrorists. He said nations like the United States, Germany and China are more restrictive with their arms sales, and as a result he said he'd only buy weapons from Israel.
The Philippine leader has been controversial for his political rhetoric and his fight against drugs.
Since he took office in 2016, Duterte has taken actions that have resulted in the deaths of thousands of suspected drug users. The war on drugs has also led to the harassment and prosecution of drug war critics and crowded jails, Human Rights Watch said.
Duterte has also come under fire for a series of undiplomatic comments, including one that said rape is inevitable as long as there are beautiful women.
In the past, Duterte has also compared his war on drugs to the Holocaust and likened himself to Hitler.
"Hitler was the devil himself," Rivlin told Duterte.
At the meeting Tuesday, Duterte mentioned his Jewish daughter and noted the Philippines broke a tie vote at the United Nations to create Israel in 1947.
Rivlin noted the countries' common bond in fighting terrorism, saying "we insist on the principles of democracy and equality."
Israel has previously faced criticism for its arms sales in 2017, when it supplied Myanmar with "advanced weapons" during fighting against the Rohingya, the country's Muslim minority.