Trump wrote on social media that he is considering stopping aid to Iraq if former Prime Minister Nouri al-Maliki is allowed to lead the country again.
"The last time al-Maliki was in power, the country was plunged into poverty and total chaos," Trump wrote.
The response on Wednesday came both from al-Maliki and from people on the streets of the capital.
"We reject the blatant interference in Iraq's internal politics and see it as a violation of the country's sovereignty," al-Maliki said in a statement.
Several hundred people gathered in protests against the United States near the country's embassy in the so-called Green Zone in Baghdad, where government agencies and embassies are located.
