According to an Iranian government statement, the male attackers had returned to the country last summer after fighting for Islamic State in Mosul, Iraq, and Raqqah, Syria, and had "intended to carry out terrorist operations in religious cities".
"Death to America", "Death to the Saud" ruling family, and "We are not afraid", shouted the crowd behind a lorry bearing the coffins of 15 of the 17 people killed.
Tehran police said the vehicle the attackers used on Wednesday was discovered on Saturday in the city centre.
On Thursday, Iran's Foreign Minister Mohammad Javad Zarif criticized the language and rejected the condolences on Twitter.
New video shows tense moments of London attack; 3 arrested
On the night of the attack, staff pretended to lock the doors in a move that was thought to protect 20 customers inside. Police also said they had made a fresh arrest on Tuesday, detaining a 27-year-old man in Barking, east London .
Lawmakers of the Iranian Parliament were briefed on the recent deadly terror attacks in the country by the Iranian intelligence and Interior Ministers as well as Deputy Commander of the Islamic Revolution Guard Corps (IRGC) Brigadier General Hossein Salami in a closed-door session of Parliament (Majlis) on Sunday. The US goal is seen variously as curbing Iran's regional role or redrawing the 2015 nuclear agreement, described by Trump in his election campaign as the "worst deal ever".
Iranian security officials counter that it is their regional rival Saudi Arabia, a close U.S. ally, that is responsible for funding and spreading the ideology that most closely resembles ISIL's. "Iranian people reject such United States claims of friendship", Zarif tweeted on Thursday.
Khomeini's successor and the current Supreme Leader, Ayatollah Ali Khamenei, as well as the speaker of Iran's parliament, Ali Larijani, both tried to downplay the seriousness of the attacks.
On Thursday, Iran's Intelligence Minister Mahmoud Alavi said investigators were working to determine whether Saudi Arabia had a role Wednesday's attacks but said it was too soon to say if that was the case.
"We are focused on intelligence" gathering, he said.
On Monday, emboldened by Trump's earlier visit and support, Saudi Arabia led several Sunni nations in isolating Qatar, due to it's good relationship with Iran particularly as the bordering nation's share and cooperate on access to the world's largest natural gas field.