Prime Minister Benjamin Netanyahu of Israel provoked strong reactions around the world when he announced at the White House this month that he had nominated President Trump for the Nobel Peace Prize.

While it drew much less attention, his suggestion during his trip to the United States that he would make a different nomination for a much more parochial honor is inflaming tensions about 150 miles north of Washington.

“Next time I’m here, we go down to Cheltenham High School, near Philadelphia, and I’ll nominate you for the hall of fame,” Mr. Netanyahu told Mark Levin, the conservative commentator, during a Fox News interview that aired Saturday.

Earlier in the interview, the men discussed their shared connection to the public high school in Cheltenham Township. Mr. Netanyahu (who graduated in 1967) was born in Israel but lived in Cheltenham for several years with his family while his father taught at a local Jewish college; Mr. Levin (class of 1974) was born and raised in the area. Mr. Netanyahu has already been inducted into the school’s hall of fame. Mr. Levin has not.

In Cheltenham, a racially and religiously diverse Philadelphia suburb, the televised reminiscence intensified a debate about whether either man deserves to be honored by their alma mater.