The Reuters news agency reported that a government media outlet quoted Assad saying that he also didn't want rebel fighters to use a cease-fire to gain ground.
"We have said that we are ready to stop military operations, but the issue relates to more important factors ... such as preventing terrorists from using it to improve their positions," Assad was quoted as saying.
The dictator refers to all those fighting against the regime as terrorists.
Meanwhile, the main Syrian opposition group said Saturday it is ready "in principle" to implement a provisional truce, slamming Russia and the Syrian government after a deadline set for a temporary cessation of hostilities passed.
The Saudi-backed group, known as the High Negotiations Committee, said any potential truce would require the Syrian government to first lift blockades from rebel-held communities and release thousands of detainees.
The statement followed a meeting among opposition groups held in the Saudi capital, Riyadh, on Saturday to discuss the situation after the passing of a deadline set by world powers, including Russia and the U.S.
A Feb. 12 meeting in Munich of 18 nations supporting opposing sides in Syria's five-year civil war agreed to bring about a cessation of hostilities within a week to allow for peace talks to resume in Geneva. But the truce never took hold amid intense fighting, including a massive Russian-backed government offensive near the Turkish border.
U.N. envoy Staffan de Mistura told the Swedish newspaper Svenska Dagbladet on Friday that he cannot "realistically" get the parties in the Syrian conflict back to the table by Feb. 25 as he had hoped.
U.S. Secretary of State John Kerry spoke with Russian Foreign Minister Sergey Lavrov on Saturday to discuss the progress made by two U.N. task forces meeting in Geneva this week to discuss humanitarian assistance and a cessation of hostilities, according to State Department spokesman John Kirby.
Although the details "are not yet fully agreed upon," Kerry expressed his hope that a full cessation of hostilities could be achieved in the shortest timeframe possible, Kirby said.
The HNC said any truce must include all parties to the conflict, notably Russia and Iran, key supporters of Assad's government. Russia has said that it would continue to strike at "terrorists" in Syria even during a cease-fire.
"The deadline set in Munich for a cessation of hostilities has passed without response from Russia or the regime, who show disdain for the international community and disregard for the lives of Syrians," said HNC spokesman Salem Al Meslet in a statement.
He said Assad and Russia have spent "yet another week annihilating defenseless Syrians" and called on the international community to implement a new approach that holds them to account.
Saudi Arabia's foreign minister meanwhile said he favors equipping Syrian rebels with surface-to-air missiles to "change the balance of power on the ground."
In an interview with the German weekly Der Spiegel published Saturday, Foreign Minister Adel al-Jubeir said the moderate opposition could "neutralize" helicopters and aircraft that have been bombing them. He said the move would have to be studied carefully, "because you don't want such weapons to fall into the wrong hands."
The U.S. has long opposed equipping rebels with such weapons, fearing they could end up in the hands of extremist groups, which could potentially use them to shoot down passenger planes.
Al-Jubeir said it's a decision that the international coalition will have to make. "This is not Saudi Arabia's decision."
Meanwhile, the spokesman for Russian President Vladimir Putin said the Kremlin is disappointed by the rejection of a proposed United Nations resolution aimed at stopping cross-border shelling and foreign ground intervention in the Syrian conflict.
The draft resolution was put forth by Russia on Friday at an emergency meeting of the U.N. Security Council and was immediately turned down by France.
It did not name Turkey but it was clearly aimed at the Turkish government, which has threatened ground action and is shelling U.S.-backed Kurdish militia positions in Syria.
On Saturday, Kremlin spokesman Dmitry Peskov said "Russia views such trans-border strikes by Turkish artillery and artillery strikes at Syrian territory as unacceptable," according to the state news agency Tass.
"We can only express our regret that this draft resolution was not supported," he said.
Syria's government meanwhile described the Turkish artillery shelling inside Syria as an "outrageous violation" of international law.
Turkey has been shelling Kurdish militia positions in Syria in recent days, saying it is exercising its right to self-defense and responding to fire from Syrian soil. It has also threatened to send in ground forces.
The main Kurdish group in Syria, the People's Protection Units, or YPG, has denied firing at Turkey from Syria. The group has been on the offensive near the Turkish border, seizing territory from Turkey-backed Syrian rebels as well as the extremist Islamic State of Iraq and Syria, or ISIS.
Turkey views the YPG as an extension of the Kurdistan Workers' Party, or PKK, which has waged a decades-long insurgency against Ankara.
The YPG dominates a military alliance made up of Kurdish, Arab and Christian fighters known as the Syria Democratic Forces, which on Friday captured the town of Shaddadeh in northeastern Syria after three days of battles with ISIS militants. The town was one of the biggest strongholds of the extremist group in Syria.
The capture of Shaddadeh was reported by the SDF as well as by Syrian activist groups opposed to Assad on Friday.
A militant website affiliated with ISIS disputed the reports, saying the militants were still in control of the town. A statement published by the Aamaq news agency said fighting was still raging around the town with Kurdish units trying to advance under U.S. air cover.
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