They said the convoy had been headed to Anas bin Malik mosque in central Damascus for Eid al-Fitr prayers marking the end of the fasting month of Ramadan.
"Regarding the information reported by Al-Arabiya, I can assure you that it is completely false," Information Minister Omran al-Zohbi told state television.
"The president arrived at the mosque driving his own car, he attended the prayer and greeted everyone in the mosque as he does every day when he meets people.
"Everything is normal," Zohbi added. "They wanted to spoil the celebrations for Syrians."
Regional powerhouse Saudi Arabia is a strong supporter of the Sunni-led rebels seeking to oust Assad who belongs to the Alawite sect, an offshoot of Shiite Islam.
Since the start of the anti-Assad uprising, Syria's regime has consistently dismissed the armed opposition as foreign-backed "terrorists".
The Syrian Observatory for Human Rights could not confirm the reported rocket attack, but said mortar rounds hit the upmarket Malki area in central Damascus, near where Assad was attending Eid prayers and where his offices are.
At least two Islamist rebel groups later claimed via Facebook to have attacked Assad's convoy.
"Liwa al-Islam used rocket fire to target the convoy, while other rebel groups used mortars," Liwa al-Islam spokesman Islam Allush told AFP via the Internet.
State television showed Assad sitting with other dignitaries, appearing relaxed and smiling during the morning prayer.
He has rarely appeared in public since the start of the conflict.
Opposition chief Ahmad Jarba, meanwhile, visited Daraa in southern Syria near the Jordanian border to mark Eid, a National Coalition source told AFP.
"This visit to the south shows that large swathes of Syria, from the north to the south, are in opposition control," the source said on condition of anonymity.
Jarba went in a village called Tal Shehab and visited schools housing refugees, the source added.
The Syrian Observatory, which compiles its information from activists and medics, said on Thursday that the conflict had claimed at least 4,420 lives during Ramadan.
While some two-thirds of the victims were combatants on both sides, this time last year most of the dead were civilians, reflecting a shift in the nature of Syria's war.
Despite international efforts to broker a negotiated end to the conflict, there is still no end to the fighting.
Washington, which has repeatedly called for Assad's ouster and Moscow, a key ally of the Syrian regime, have tried without success so far to organise a peace conference in Geneva.
US President Barack Obama and Turkish Prime Minister Recep Tayyip Erdogan discussed Syria by phone on Wednesday and "agreed on the importance of supporting a unified and inclusive" opposition, a White House statement said.
Meanwhile, diplomats told AFP that Moscow has rejected a Saudi proposal to abandon Assad in return for a huge arms deal and a pledge to boost Russian influence in the Arab world.
The reports come nine days after President Vladimir Putin, a strong Assad backer, met influential Saudi intelligence chief Prince Bandar bin Sultan.
At Kremlin talks, Bandar proposed that Riyadh buy weapons worth $15 billion from Moscow and invest "considerably" in Russia, said a European diplomat who shuttles between Beirut and Damascus.
The prince also reassured Putin that "whatever regime comes after" Assad will be "completely" in the Saudis' hands and will not sign any agreement allowing any Gulf country to transport gas across Syria to Europe in competition with Russian exports.
An Arab diplomat with contacts in Moscow said Putin refused, telling Bandar that Russia would not change its stance.
"Bandar bin Sultan then let the Russians know that the only option left in Syria was military and that they should forget about Geneva because the opposition would not attend."