Syrian state media SANA said the attack on Saturday took place in the Mazzeh neighbourhood. It said “Israeli aggression” targeted the building.
Iran also blamed Israel for the attack, saying it “reserves the right to respond”.
“The Islamic Republic will not leave the Zionist regime’s crimes unanswered,” Iran’s President Ebrahim Raisi said in a statement broadcast on state media.
Earlier, the foreign ministry spokesman Nasser Kanani said Tehran would respond “at the appropriate time and place”, and condemned “an escalation in aggressive and provocative attacks” by Israel.
A well-informed source told Al Jazeera the target was an IRGC intelligence unit, adding that a senior IRGC intelligence official in Syria and his assistants were in the building.
In a statement immediately after the attack, the IRGC said an air raid by Israeli fighter jets killed “a number of Syrian forces and four military advisers”. It identified the people killed as Hojjatollah Omidvar, Ali Aghazadeh, Hossein Mohammadi and Saied Karimi, without sharing their ranks.
Later in the day, IRGC said a fifth member of the elite force also died after succumbing to his wounds, naming him as Mohammad Amin Samadi, Iranian state media reported.
The attack, which is believed to have been carried out with at least four missiles, completely destroyed a four-storey building, according to Iranian state media.
Israel has yet to comment.
Widening tensions
The attack in Syria comes amid widening tensions in the region and the Israeli offensive on Gaza that has killed nearly 25,000 people.
On Saturday, an Israeli raid in south Lebanon killed two people, at least one a Hezbollah member. Such attacks in the past have targeted members of Hezbollah as well as the Palestinian group Hamas.
Al Jazeera’s Imran Khan, reporting from the southern Beirut neighbourhood of Borj el Barajneh, said Israel had struck deeper into Lebanese territory than usual, some 25km (15.5 miles) from the disputed border area.
“However, these attacks can happen,” Khan said, citing above all the assassination of Hamas deputy leader Saleh al-Arouri in Beirut.
In Iraq, missiles fired on Saturday at US-led coalition forces stationed in the Ain al-Asad air base also raised further fears of a wider regional conflagration.
US officials said initial assessments suggested US personnel suffered minor injuries and a member of Iraq’s security forces was seriously wounded. It was not clear whether the base was hit by ballistic missiles or rockets.
Reporting from Baghdad, Al Jazeera’s Mahmoud Abdelwahed said the base, a major military hub hosting US troops, has been the target of previous attacks carried out by Iran-backed armed groups, who “accuse the US of [being] a major supporter of Israel’s military campaign against Gaza”.
Tensions have also been escalating in the Red Sea amid attacks on commercial ships by the Iran-aligned Houthi group in Yemen. US Central Command forces on Saturday struck a Houthi anti-ship missile that was aimed into the Gulf of Aden and prepared to launch, the US military said.
The Houthis, who control most of Yemen, say their attacks are in solidarity with Palestinians under attack from Israel in Gaza. Since last week, the US has been launching attacks on Houthi targets in Yemen, and this week returned the rebels to a list of “terrorist” groups.
Jordanian foreign minister Ayman Safadi told Al Jazeera that the war on Gaza carried the very serious risk of spilling over the rest of the region. “The Israeli prime minister might be consciously provoking confrontations on other fronts, particularly with Lebanon and other parts of the region, to delay the political reckoning that he will have to face,” he said, referring to corruption charges against Benjamin Netanyahu.
“Netanyahu may be looking to provoke other fronts into which he will drag the West,” he said. “Then we will be looking at a very serious escalation.”