Louis Sako described the campaign launched by America and other countries including Britain as a "dirty political game".
"Bombing these jihadists will not make them disappear, that's for sure," he said.
Islamic State extremists have taken over many parts of Iraq and Syria as the militants seek to create an new state ruled by Islamic law.
Patriarch Sako said: "Many innocent individuals risk being killed. Infrastructures are destroyed and will remain destroyed.
"The Americans have already done this: they destroyed the country and did not rebuild it.
"The most serious part of it all is that now everyone is saying the war is going to go on for years.
"This sends out two different and very dangerous messages simultaneously.
"The message to jihadists is: don't worry, you have plenty of time to get organised, get more money together and enlist more paid militants.
"The message to the refugees is: this situation's going to go on for years, the only future you have is away from here, away from your homes.
"It's best if you leave if you can."
The patriarch called for better education and training for young people in the Middle East and said this was the only way to show 'how false and monstrous this bloodthirsty ideology really is'.
A US-led coalition is continuing to carry out air strikes on the militants in Iraq and Syria.