Assad spoke to U.N. Special Envoy Lakhdar Brahimi and told him support for "terrorist" elements in his country must end before peace negotiations can begin.
"The success of any political solution is tied to stopping support for terrorist groups and pressuring their patron states," he said.
Assad has increasingly positioned himself as fighting against extremist al-Qaida elements seeking control of the country, The New York Times reported.
The remarks come a day after the Assad regime fired a deputy prime minister who said he met with the U.S. ambassador to Syria about proposed peace talks to end the conflict.
Deputy Prime Minister for Economic Affairs Qadri Jamil was dismissed for spending too much time outside the country, neglecting his duties and holding meetings "without authorization from the government," the regime's Syrian Arab News Agency and state TV reported Tuesday.
Jamil told reporters in Moscow Monday he met with U.S. officials about the peace talks between Assad's regime and the Syrian opposition proposed by Washington, Moscow and other world powers to be held in Geneva, Switzerland, in late November.
He separately told Lebanon's pan-Arabist al-Mayadeen TV he also met with a Russian diplomat and U.N. officials. He did not say if he coordinated his moves with the Assad regime.
"I am not an employee," he told the network. "I am a political activist."
Jamil, a Moscow-educated economist, was one of two members of an internal political opposition Assad added to his regime last year in a move billed as broadening its base.
She called the meeting one "in a long list of meetings that we've had with officials who have connections with the regime and, of course, with the opposition."
Psaki said she couldn't comment on a report Jamil tried unsuccessfully to persuade Ford to let him attend the peace talks as an opposition member.
Neither the armed opposition nor the main non-violent umbrella National Coordination Committee for the Forces of Democratic Change accepts Jamil as an opposition member.
Jamil told Russia's state-funded RT news channel he proposed joining the opposition delegation at the peace talks and indicated Ford told him he couldn't represent both sides at once.
He said Washington "misunderstood" the nature of his political orientation as an internal opposition figure.
"They wanted us to go [to Geneva] as part of the government delegation," Jamil said, adding, "We agree with the government on about 10 percent" of its policies.
Jamil told al-Mayadeen it made little sense to him for the Assad regime, which has said it will attend the so-called Geneva 2 talks, to blame him for meeting with the talks' sponsors.
He said he was working to "end the bloodbath in Syria."