Iranian diplomats blamed the abduction, from close to the Shia shrine of Sayyida Zainab, on “armed groups”.
Syrian state television later gave the same account of the incident.
Meanwhile, fresh fighting has been reported around Damascus, and in the northern city of Aleppo, where rebels are trying to secure their positions.
The Iranian consul in Damascus said the whereabouts of the abducted pilgrims was known.
Syrian state-run news agency Sana said the Iranians had been kidnapped by “armed terrorist groups” and that Syrian authorities were “working to handle the situation”.
Thousands of Iranians travel each year to Syria to visit the pilgrimage site in the mostly Shia district of Sayyida Zainab, which has seen heavy fighting in recent weeks.
There have been several other reports of groups of Iranian pilgrims being kidnapped in Syria in recent months, with most later being freed.
In May, 11 Lebanese Shia pilgrims were abducted in Syria while returning from Iran.
They were released after being held for three days, but the incident sparked violence across Lebanon, where the crisis in Syria has heightened sectarian tensions.
Meanwhile, fresh fighting was reported in Syria’s two biggest cities on Saturday.
Most areas of Aleppo where rebels are entrenched have been bombarded by government forces and clashes have been reported in several districts.
Video footage posted by activists showed a military jet flying over what they said was the rebel-held quarter of Salah al-Din followed by a loud explosion.
Activists reported clashes in several areas too, including around the officers’ club and a political security headquarters.
Government forces seem to now be pushing harder in the crucial battle for Aleppo.
Syrian state television reported that troops had inflicted huge losses on what it called “terrorist mercenaries” in Salah al-Din and in other nearby areas too, our correspondent adds.
There have been skirmishes in which rebels have done rather well, he says, seizing three police stations and retaking a fourth on Friday, and rebels are “incrementally” increasing the size of the area they hold.
The rebels have “remarkable” defence capability in Salah al-Din where government tanks had been trying to enter, but as an area full of narrow twisting lanes, it is perfect for guerrilla warfare, he adds.
However, the full thrust of the armour and the artillery from the regime side has not been seen yet, he adds.
The focus of the fighting is also on the southern edge of Damascus where shelling and gunfire were reported from the Tadamon quarter, despite it having been earlier stormed by government forces.
Shooting and explosions were also being heard in some central parts of the capital, and activists reported clashes too on the western side of the city, in and around Dumar.
Earlier, Russia and China condemned a UN General Assembly resolution passed on Friday which criticized the Security Council for failing to halt the violence in Syria.
Moscow’s UN envoy, Vitaly Churkin, told reporters the resolution was one-sided and supported the armed opposition.
Western nations praised the resolution, which passed by 133 votes to 12 with 31 abstentions.
It criticizes both the UN’s own Security Council and the government of Syrian President Bashar al-Assad for its use of violence.
The assembly debated the resolution, which was proposed by Saudi Arabia, shortly after the resignation of UN-Arab League envoy Kofi Annan and the failure of his six-point peace plan.
Activists say more than 20,000 people – mostly civilians – have died in 17 months of unrest.
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