"We cannot start any political solution while terrorism is still rampant in Syria," Foreign Minister Walid Mualem told the UN General Assembly.
The statement killed off prospects for a resumption of peace talks in the near future despite efforts by UN peace envoy Staffan de Mistura, who was appointed in July to re-start negotiations.
Mualem dismissed the Syrian opposition recognized by the West to attend the peace talks, saying it lacked credibility and followed "the orders of its Western masters."
"We are open to a political solution in Syria, with a real opposition ... that does not depend on the outside," he said.
The West is stepping up aid to the moderate Syrian opposition, including military training to be provided by the United States to put more rebel forces on the ground to confront the jihadists.
Mualem hit out at countries supporting the Islamist groups, in an implicit attack on Gulf countries where the so-called Islamic State (IS) group and Al-Nusra Front have drawn financial and military backing.
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Combating the Islamist threat "is certainly possible through military strikes," said Mualem.
"But most importantly, to do so through stopping states that arm, support, train, fund and smuggle those terrorist groups," he said.
The UN Security Council has adopted a resolution demanding that countries take action to choke off financial support and the flow of foreign fighters.
But Mualem said the resolution was "unimplemented."
He warned that without action to cut off the Islamists from their sponsors a military campaign "will create a whirlpool of which the international community will not exit in decades."
The foreign minister, who is also deputy prime minister, spoke at the UN podium as IS fighters closed in on the key Kurdish town of Ain al-Arab in northwest Syria, known as Kobane to the Kurds.
The US-led coalition carried out a fresh round of airstrikes, nearly a week after it began hitting jihadist positions in Syria, expanding an air campaign launched in August in Iraq.