Iran’s Revolutionary Guards ratcheted up the tensions with Saudi Arabia as it accused Tehran’s regional rival of involvement in Wednesday’s double terrorist attack in the capital, which left at least 13 people dead and wounded more than 50.

Gunmen and suicide bombers launched simultaneous attacks on the parliament building in Tehran and the nearby shrine of Ayatollah Ruhollah Khomeini, the Islamic Republic’s founder.

The attacks were claimed by Isis, in what would be the jihadi group’s first significant strike in the Islamic Republic. However a statement from the Revolutionary Guards linked the “brutal attack” to Donald Trump’s visit last month to Riyadh, where the US president singled out Iran for fuelling “the fires of sectarian conflict and terror”.

“This terrorist act took place a week after a joint meeting between the US president and head of a reactionary regional country [Saudi Arabia] which has been a constant supporter of terrorism,” the statement said. “The fact Isis claimed responsibility proves that they [Saudi Arabia] were involved in the brutal attack.”

Speaking in Berlin, Adel Al-Jubeir, Saudi Arabia’s foreign minister, denied the accusation of involvement and said there was no evidence that his country was involved. “We condemn terrorist attacks anywhere they occur and we condemn the killing of the innocent anywhere it occurs,” Mr al-Jubeir was quoted by Reuters as saying.

Hassan Rouhani, Iran’s president, condemned the attacks, without laying the blame at the feet of Saudi Arabia. However, the accusation from the powerful Revolutionary Guards will stoke the increasingly bitter enmity between Tehran and Riyadh, which are involved in proxy wars from Syria to Yemen.

Iran’s foreign minister, Mohammad Javad Zarif, tweeted, “Terror-sponsoring despots threaten to bring the fight to our homeland. Proxies attack what their masters despise most: the seat of democracy.”

Mr Zarif seemed to be pointing at a comment last month by the Saudi deputy crown prince Mohammed bin Salman that any struggle for influence between Riyadh and Tehran would take place “inside Iran, not in Saudi Arabia”.

“We know that the aim of the Iranian regime is to reach the focal point of Muslims [Mecca] and we will not wait until the fight is inside Saudi Arabia and we will work so that the battle is on their side, inside Iran, not in Saudi Arabia,” Prince Mohammed said in a television interview.

The attacks also come at a sensitive moment in the Gulf, where a new rift opened this weekpitting Qatar, with whom Tehran has ties, against Saudi Arabia, the United Arab Emirates, Egypt and Bahrain. The quartet on Monday severed diplomatic ties with Qatar and accused Doha of supporting terrorism.

Hamid-Reza Taraghi, a senior politician close to Tehran’s hardliners, blamed a combination of Saudi Arabia, the US, Isis and the exiled opposition group MEK for Wednesday’s attacks. “Saudi Arabia is definitely playing the leading role in these incidents, considering that its foreign ministry threatened Iran two to three days ago,” he said, referring to a call by Riyadh for Iran to be punished for supporting terrorism. He provided no evidence to support his claims.

His view was echoed by others, though they did not provide evidence either. “The fact that these two attacks took place . . . after that [Riyadh] meeting means that both the US and the Saudi regime have ordered their proxies to embark on that act,” Brigadier-General Hossein Nejat of the Revolutionary Guards told a local news agency.

Mohsen Rezaei, a former Revolutionary Guards commander, warned terrorists to expect a “tough and unforgettable” response from Iran.

Mr Trump’s administration is viewed as much more hawkish on Iran than the previous government of Barack Obama. Tehran has long accused Saudi Arabia of supporting Isis.

The assault began at 10.30am local time when three gunmen (earlier reports had said four) in women’s clothing walked into the building and began shooting. One detonated an explosive vest. All the attackers were killed after a stand-off lasting several hours, Iran’s interior ministry said.

Two further gunmen also opened fire at the Ayatollah Khomeini shrine in the Iranian capital. One was reported to have killed himself by detonating an explosive vest. Another was shot dead. Based on a video released by Isis, the attackers spoke Arabic. Brigadier-General Nejat said the nationality of the attackers was not yet clear, but an Iranian official told state television on Wednesday night that they were Iranian.

At least 13 people were killed in the two attacks, Pir-Hossein Kolivand, head of Iran’s emergency department, was quoted as saying by the official Irna news agency on Thursday.

Isis on Wednesday vowed further attacks on Iran, saying “Persia should know that the state of the caliphate will not miss an opportunity for an onslaught against them”.

Iranian officials said security forces remained on high alert.

Terrorist attacks are rare in Iran, which keeps a tight grip on domestic security. The country has largely been spared from militant attacks despite its heavy support of Shia militias in Syria and Iraq, which has increased sympathies among some of those countries’ Sunni populations for radical groups such as Isis.

If Iran steps up its fight against Isis in the wake of Wednesday’s attack, the situation in the region could become even more volatile, analysts say. Charlie Winter, senior research fellow at the International Centre for the Study of Radicalisation at King’s College London, said the attack could boost Isis’s flagging morale and intensify pressure on Tehran to step up its involvement in Syria against the jihadis. “If this happens, a more intense ‘Sunni war against Shia Islam’ will pour petrol on Isis’s ideological fire,” he said.

Security analysts outside of Iran have long argued that it has not been attacked because it tolerated the presence of al-Qaeda and the movement of communications and finances through the country. But for Isis, which is not reliant on foreign financing, Iran has long been a target.

While it is difficult to gauge the extent of an Isis presence in Iran, the group has long sought to attract people from Iran’s Sunni minority. Last March, it released a 36-minute video in Persian, vowing to conquer Iran. In the video, militants used photographs of Iranian leaders for target practice, including Qassem Soleimani, commander of the Revolutionary Guards’ elite Quds force.