The American Jewish Committee has criticised the US president over the remark, adding that his words could “feed bigotry”.
Mr Netanyahu is the current leader of Israel, but Jews born or living in other countries do not regard him as their prime minister.
Mr Trump was speaking to the Republican Jewish Coalition in Las Vegas on Saturday when he said: “I stood with your prime minister at the White House to recognise Israel’s sovereignty over the Golan Heights.”
The Golan is a plateau in southwest Syria which was captured by Israel in 1967 and annexed in 1981.
The American Jewish Committee wrote on Twitter on Sunday: “Mr President, the prime minister of Israel is the leader of his (or her) country, not ours.
“Statements to the contrary, from staunch friends or harsh critics, feed bigotry.”
Israel is holding a general election in the coming days, with Mr Netanyahu vowing to “impose sovereignty” on the occupied West Bank if he is returned to office.
The incumbent faces a tight race against former military chief Benny Gantz, although his Likud party has a better chance of forming a ruling coalition, according to polls.
Mr Trump also appeared to conflate the Republican group in Las Vegas with all US Jews when he asked how they could have supported his predecessor.
He said: “How the hell did you support President Obama? How did you do it?”
Members of the coalition reportedly shouted back: “We didn’t.”
US Jews overwhelmingly backed Mr Obama in both the 2008 and 2012 elections.
Mr Trump took aim at the opposition in his speech on Saturday, and said: “The Democrats have even allowed the terrible scourge of antisemitism to take root in their party and in their country.”
The US president also poked fun at Democratic representative Ilhan Omar, who has been accused of making antisemitic remarks.
He said: “And a special thanks to Representative Omar of Minnesota.
“Oh I forgot, she doesn’t like Israel I forgot. I’m so sorry.”
Mr Trump later touched on the issue of migrants entering the US across the southern border, and painted a picture of what he suggests a Central or South American migrant might look like.
He said: “We don’t love the fact that he’s got tattoos on his face, that’s not a good sign.
“We don’t love the fact that he’s carrying the flag of Honduras or Guatemala or El Salvador, only to say that he’s petrified to be in this country.
“The asylum programme is a scam, [the migrants are] some of the roughest people that you have ever seen, people that look like they should be fighting for the UFC.”
Mr Trump’s comments came after he declared “our country is full” as he inspected a refurbished section of steel fencing along the Mexican border on Friday.