At least 71 people have died in blasts near the Shia shrine of Sayyida Zeinab, south of Syria's capital Damascus.
A bus station and a building housing military headquarters were hit by the blasts, which mangled nearby vehicles.
It happened as the government and opposition groups gathered in Geneva in a bid to start talks aimed at a political solution to the conflict.
The attack, claimed by the Islamic State group, was aimed at disrupting the talks, the EU said.
Both the Syrian government and opposition are in Geneva but the talks have yet to begin. The main opposition group says the government must first meet key humanitarian demands.
US Secretary of State John Kerry urged both sides to seize the opportunity to end the bloodshed.
Mr Kerry said there was "no military solution" to the spiralling crisis, which he warned could engulf the region if the tentative UN-sponsored negotiations fail as previous attempts have.
The UN envoy to Syria has scheduled separate discussions with both sides in Geneva on Monday.
Sunday's attacks near Sayyida Zeinab were carried out by two suicide bombers, but some witnesses spoke of three blasts.
The UK-based Syrian Observatory for Human Rights said that, of the 71 people killed, 42 were fighters loyal to the Assad regime. The group said another 29 civilians, including five children, died.
The blasts took place several hundred metres from the golden-domed shrine, which was not itself damaged - although it has been previously targeted, most recently in February last year.
It contains the grave of one of the Prophet Muhammad's grand-daughters and continues to draw many Shia pilgrims, despite the civil war.
At the scene: Rami Ruhayem, BBC Arabic, south-eastern Damascus
The destruction is huge. The building in front of me on Koua Soudan Street is charred black in the middle. I'm told that there is a military headquarters on the ground floor and families also lived in the five-storey building.
There is a fruit stall with blackened oranges all over the floor.
I can also see a large number of charred vehicles, including a bus in the middle of the street which is almost completely destroyed and overturned. The smoke is still rising from one of the cars on the side of the street.
BBC Arab affairs editor Sebastian Usher says Shia fighters from around the region have joined the conflict in Syria on the grounds that they wish to protect the shrine from the civil war.
The Lebanese Shia movement Hezbollah has cited it as a key reason that it chose to fight on the side of President Bashar al-Assad, he adds.
More than 250,000 people have died and 11 million have fled their homes in almost five years of civil war in Syria. The violence has also been the biggest driver behind Europe's migration crisis.
Geneva peace talks
Who is attending? Delegates from the Syrian government and the main opposition bloc, the High Negotiations Committee (HNC). Other opposition figures have been invited as advisers.
Who is not attending? Syrian Kurdish group the PYD (regarded by Turkey as a terrorist group); so-called Islamic State (IS); al-Nusra Front.
What is being discussed? A possible ceasefire; release of prisoners; aid deliveries to the worst-hit areas; the threat from IS.
The bombings were "clearly aimed to disrupt the attempts to start a political process" in Geneva, said EU foreign policy chief Federica Mogherini.
The initiative got off to a shaky start after the opposition High Negotiations Committee (HNC), backed by Saudi Arabia, only agreed late on Friday that it would travel to Geneva - hours after the Syrian government delegation had arrived and held preliminary talks with UN envoy Staffan de Mistura.
The HNC had been under considerable pressure from Saudi Arabia and the US to attend.
Hostility between key players remains high, with the Syrian government's envoy Bashar al-Jaafari saying the HNC's last-minute decision to take part showed it was "not serious".
He said the Sayyida Zeinab attack confirmed the link between the opposition and terrorism.
Nevertheless, he was also quoted as saying the government was "absolutely" considering humanitarian moves such as the creation of humanitarian corridors, ceasefires and prisoner releases.
The urgent need for humanitarian steps in Syria has been highlighted by the plight of starving residents of the besieged town of Madaya, and the HNC has made them a condition of negotiations.
Mr Kerry had blunt words about the regime's tactics, saying they ran directly counter to the rules of war by forcing residents to choose between surrendering or starving in towns such as Madaya.
Mr Mistura described the talks as "a good start" and told the BBC he was "optimistic". He said the HNC would give more details later.
The so-called proximity talks are expected to last six months, with delegations sitting in separate rooms and UN officials shuttling between them.
UN chief Ban Ki-moon called on all sides to put the interests of Syrians above their own.
"Children and women in particular have borne the brunt of this fighting and it is time now to see the end of the fighting and other human rights abuses that have dominated the war," he said.