The UAE state news agency WAM said President Sheikh Khalifa bin Zayed al-Nahayan had condemned "the horrific crime".
In a condolence message ahead of a funeral for the victims, Ayatollah Ali Khamenei said the attack: "will not damage the Iranian nation's determination and the obvious result is nothing except an increase in hate for the governments of the United States and their stooges in the region like Saudi (Arabia)", state media reported.
Alavi told state TV that authorities had found and raided the home where the pre-attack IS video was filmed.
Riyadh and Teheran vie for predominance in the Gulf and influence in the wider Islamic world. It was the first time the terrorists targeted Iran, which provides ground forces against Daesh and other terrorist groups in Syria and Iraq.
Iran blamed the Wednesday attacks on Saudi Arabia, casting them in the context of a broader regional conflict that encompasses the war inside Syria. Iran also has been fiercely opposed to the militant group.
The Parliament assault began when four armed assailants, dressed as women, burst into the building complex and attacked the parliament buildings in the morning, reports Tasnim news.
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The assault was the first claimed by the Islamic State group in Iran, and was the worst terror strike to hit the nation in years.
On Thursday, the Iranian Intelligence Ministry released the names of the five terrorists who were killed after carrying out the deadly attacks in Tehran.
"Iranian people reject such USA claims of friendship", Zarif tweeted.
Iran's emergency services said a total of 13 people were killed in the two attacks and 46 wounded.
"We underscore that states that sponsor terrorism risk falling victim to the evil they promote".
Police on Thursday said they now held six suspects as part of their investigation into the attacks.
"For these two actions to happen... after this meeting means that the U.S. and Saudi regimes had ordered their stooges to do this", said Mohammad Hossein Nejat, deputy head of the Revolutionary Guards intelligence branch, according to the Fars news agency. Some pointed to comments in May by Saudi Deputy Crown Prince Prince Mohammed bin Salman, the son of the King Salman and the kingdom's defense minister, who said his country would "work so that it becomes a battle for them in Iran and not in Saudi Arabia".
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