"We grieve and pray for the innocent victims of the terrorist attacks in Iran, and for the Iranian people, who are going through such challenging times", Trump said in a brief statement.
"Let there be no doubt that we will take revenge for today's attacks in Tehran, on terrorists, their affiliates and their supporters", Brigadier General Hossein Salami was quoted as saying by state media.
Deputy Interior Minister Mohammad Hossein Zolfaghari told Iran's state TV the apparently male attackers wore women's attire.
"I condemn in the strongest terms the attacks in the Iranian parliament building and the tomb of the revolutionary leader (Ayatollah Ruhollah) Khomeini", he said in a statement.
Iran's semi-official Tasnim news agency said the siege at parliament was over and that four attackers had been killed.
"At this hard time, I express my condolences and my solidarity to Your Excellency and the people of Iran as well as the families of all the victims, while wishing all those wounded a speedy recovery", concluded the letter.
Meanwhile, another attack took place at the Imam Khomeini Shrine, which involved armed terrorists, suicide bombers. A voice on the video says in Arabic: "Do you think we will leave?"
Fars reported that three attackers had opened fire on visitors at the shrine, while a fourth blew himself up outside a police station across from the site.
Assailants reportedly killed a security guard and wounded 12 other people, and a suicide bomber also detonated an explosive vest. "We need to give Iran the opportunity to recover and set a new course".
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Saudi Arabia's foreign minister, Adel Al-Jubeir, has denied that Riyadh was involved in the attacks.
An Associated Press reporter saw security forces, some uniformed and others in plainclothes, around the large and ornate shrine located just outside the capital.
An Iranian policeman holds a weapon as he stands by a window at the Iranian parliament in the capital Tehran on June 7, 2017, during an attack on the complex.
"Some coward terrorists infiltrated one of the buildings of Parliament".
The same news agency added that one attacker had committed suicide by swallowing a cyanide pill, while a female terrorist had been captured by the authorities.
Both attacks were claimed by Islamic State (IS, formerly ISIS/ISIL), the jihadist organization based in Iraq and Syria.
IS earlier claimed the attacks - a first for Iran - and threatened further assaults on Iranian Shia Muslims.
The attacks could also exacerbate tensions in Iran between newly re-elected President Hassan Rouhani, a pragmatist, and his rivals among hardline clerics and the Revolutionary Guards.
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