Gunmen disguised as soldiers attacked the annual Iranian military parade Saturday in the country's oil-rich southwest, killing several people and wounding otehrs in the bloodiest assault to strike the country in recent years.
Officials and an eyewitness said the gunmen were dressed in Iranian military uniforms and sprayed the crowd with gunfire using weapons they had stashed in a nearby park.
Islamic State in Iraq and Syria militants also claimed responsibility.
"One of the countries in the south of the Persian Gulf took care of their financial, weaponry and political needs", said Rouhani.
He added: "The small puppet countries in the region are backed by America, and the United States is provoking them and giving them the necessary capabilities". "It is the Americans who incite them".
"The United States condemns any terrorist attack anywhere, period".
He added that some regimes such as the USA have been overlooking this clear reality over the past four decades and are still considering support for extremist and terrorist groups as a strategic tool to promote their own goals while chanting anti-terror slogans.
Giuliani has made similar comments before on Iran, and the State Department has said he does not speak for the administration. "The attack will strengthen the IRGC's position inside Iran and in the region", Tehran-based political analyst Hamid Farahvashian said.
Iran's Foreign Ministry spokesperson Bahram Qasemi called on Denmark and the Netherlands to extradite the "perpetrators and their accomplices" to stand trial, IRNA reported.
Iran on Sunday summoned the top diplomat of the United Arab Emirates over a tweet attributed to a UAE writer on the weekend's attack on an Iranian military parade in Ahwaz province.
The British foreign ministry said its charge d'affaires had extended its condolences to Tehran and that Iranian officials were planning to lodge a formal complaint with Britain's media watchdog Ofcom.
Iran's Deputy Foreign Minister Abbas Araghchi later said the UAE ambassador would be summoned over "partial statements" in support of the group behind the attack, without elaborating.
Their funerals will be held on Monday.
Iran's Revolutionary Guards vowed on Sunday to wreak "deadly and unforgettable" vengeance for the attack, which killed 12 of their comrades.
Iran backs militant groups across the region.
Sherkarchi said that among the dead there is a small girl and a disabled veteran.
Attacks by Kurish rebels on military patrols along the border in mainly ethnic Kurdish areas further north are relatively common.
It was one of the worst ever attacks against the Islamic Revolutionary Guards Corp, the sword and shield of Shia clerical rule in Iran since its 1979 Islamic Revolution.