The two diplomats made the remarks at a press conference after their meeting earlier in which they discussed topics such as Iran's nuclear program, combating extremism and other regional issues.
The statement came in response to recent reports of unknown aircraft dropping weapons and equipment to ISIL forces in Iraq.
Jaafari said that there was no concrete evidence for the event, but he warned against the act, saying that any country supporting extremist organizations is an enemy of Iraq. Although Iraq welcomes support from all countries to fight against extremism, it does not allow any interference in its internal affairs.
"We have heard of this bad news, but it is not certain for now which countries are involved. What I would like to stress now is that if any country is confirmed to have been involved, we will clearly make our stand and firmly oppose and object to these countries for they have directly or indirectly violated Iraq's state sovereignty by supporting extremism," he said.
Iran has expressed its support for Iraq's battle against extremism and offered weapons to Kurdish forces in the north. On his visit Tuesday, Zarif said Iran will continue offering necessary support to Iraq. He also called on the international community to cut off all support to extremist groups.
"We believe that the entire international community needs to participate actively in this struggle against Daesh (Arabic acronym for the ISIL group) and terrorism and extremism. First and foremost, by ceasing to provide assistance to these terrorists, whether it is free passage, whether it is financial assistance, other types of assistance, which unfortunately have been continuing to arrive and to be received by Daesh," said Zarif.
Iraq has a clear stance to respect all countries' sovereignty and not to interfere in their internal affairs, Jaafari said in response to a question about Turkey's operation late Saturday inside Syria to bring remains of an Ottoman founder.
Zarif also said Iran respects the sovereignty of countries. "According to Iran, the respect of countries' sovereignty and territorial integrity is a basic principle of international relations. To break this rule leads to a lack of confidence," he said.
Zarif also met Iraqi Prime Minister Haider al-Abadi, saying Iran will not leave Iraq alone in the fight against terrorism.
The Iraqi premier, for his part, highlighted Iran’s role in the campaign against terrorism and underlined the need for cooperation among countries in the Middle East to fight the menace.   
Abadi also praised Iran’s assistance to his country in countering terrorism and called for promotion of ties between the two neighboring states in all areas.