The head of Iraq's delegation said Olympic chiefs had rejected their request not to display Israel's flag next to Iraq's during the Paris Games.
Iraq's men's football team beat Ukraine 2-1 on Wednesday in Lyon and lost 3-1 to Argentina on Saturday.
"When we arrived at Lyon Stadium (Wednesday), we found the Iraqi flag displayed next to the Israeli flag," despite Israel's team not having any matches in Lyon, Herda Raouf told AFP.
Raouf, whose country does not recognise the Israeli state and supports the Palestinian cause, added that his delegation had asked a representative of the International Olympic Committee (IOC) "to relocate or remove the Israeli flag," but their wish was denied.
The committee's representative argued, according to Raouf, that the "flags of all participating countries in the men's and women's football games needed to be displayed in alphabetical order".
Raouf added that his delegation sent a formal protest by email to the IOC with the same demand before the game with Argentina, but the request was once again rejected.
French security forces identified the Ukraine-Iraq and Israel-Mali football matches on Wednesday as high-risk events.
Around 1,000 French police officers were on duty to provide security at Israel's game against Mali, at which fans flew Palestinian and Israeli flags.
The Palestine Olympic Committee wrote to the IOC last week asking for a ban on Israeli athletes at the Paris Olympics over the war in Gaza, which was rejected.
Following a 1-1 draw with Mali, Israel's team are in action against Paraguay on Saturday in Paris.