According to reports the protesters moved past police in riot gear but were penned in several times throughout the night.
Police said the demonstration was “an unlawful assembly” and they could be heard shouting “move”.
The Israeli consulate said: “We are appalled to see violence during the protest in front of our offices. This is anything but peaceful and completely contradictory to the spirit of the DNC. This vocal minority does not represent the vast bipartisan majority of Americans who stand strong in support of Israel.”
It added: “It was incredibly heartwarming to see many Americans countering this hate in front of our office, echoing the strong bond between America and Israel.”
The Israeli consulate has been the target of a number of demonstrations since October 7.
Video footage from the scene shows protesters setting fire to an American flag.
Others waved Palestinian flags and posters calling to “bring the war home” with a graphic of a masked gunman.
Elan Carr, CEO of the Israeli-American Council, told the Times of Israel the pro-Palestinian protesters were “fringe crazies”.
Carr said that US leaders needed to “stand unequivocally with the state of Israel”.
Counter protesters gathered nearby and were heard calling for the return of the hostages held in Gaza.