In his first public comments on the mass migration, Assad said Europe could expect more refugees.
Countries including the US, Turkey and Saudi Arabia want to see Assad gone from power and have supported the opposition to his rule during the four-year-old war, including some of the armed groups fighting him.
Assad said Turkish support had been crucial to the growth of two of the biggest insurgent groups in Syria, IS and the al-Qaida-linked Nusra Front, and aerial bombing by a US-led coalition had failed to stop IS.
Turkey denies the accusation.
The Syrian president dismissed Western suggestions that his government’s actions in the war had fuelled the spread of such groups.
“As long as they follow this propaganda, they will have more refugees,” Assad said in an interview with Russian media.
“If you are worried about them, stop supporting terrorists.”
The Syrian government describes all the armed groups fighting it as terrorists.
The insurgents in Syria range from the hardline IS to nationalists viewed as moderate by the West.
Assad has been buoyed in recent weeks by signs of increased military support from his ally Russia. In his comments he made no mention of reports of Russian military activity in Syria.
The White House said it wanted to see Russia engage constructively with the international coalition fighting IS, rather than build up its own military presence.
Moscow says the Syrian government should be part of a broad coalition to fight IS. Assad said there was no co-ordination between his government and the US, even indirectly, apparently backing away from comments earlier this year suggesting there had been some contact.
“There’s not a single co-ordination or contact between the Syrian government and the US government or between the Syrian army and the US army. Not even any third party including the Iraqis,” he said.
He said he would only quit power if the Syrian people wanted him to and not under pressure from the West.