"One instance is the sanctions it has imposed on Iran, unreasonably seeing itself as the leader of the world," he said.
His comments comes a day after Russia and Iran renewed their support for the Syrian government in a flurry of calls on Sunday.
The allies said last week's US missile strike violated Syrian sovereignty but failed to boost the morale of "terror groups" in Syria.
In a phone call with the Syrian President, Rouhani called the strike on Friday a "blatant violation" of Syrian sovereignty.
The government refers to all those fighting against it as terrorists.
A statement carried on the military media arm of Hezbollah condemned the American strike in much stronger language, saying it had "crossed red lines" and vowing to "reply with force" to any future aggression "in a variety of ways."
"What America waged in an aggression on Syria is a crossing of red lines. From now on we will respond with force to any aggressor or any breach of red lines from whoever it is and America knows our ability to respond well," a statement published on media outlet Ilam al Harbi (War Media), reads.
Washington said the missiles were in retaliation for a chemical attack on civilians in the rebel-held town of Khan Sheikhoun last Tuesday, which left more than 80 people dead including several children.
The Iranian President's comments come despite the White House warning Syria that further use of chemical weapons or barrel bombs could bring US military retaliation.
Broadening its warning to Assad, White House spokesman Sean Spicer said that such attacks were unacceptable.
"If you gas a baby or drop a barrel bomb onto innocent people, you will see a response from this president," Spicer said.
Defence Secretary Jim Mattis said the US cruise missile strike on a Syrian air base last week damaged or destroyed 20 per cent of operational aircraft, as well as fuel and ammunition sites and air defence capabilities.
Earlier yesterday, a US military spokesman said the United States military is still able to deconflict operations with Russia over Syria, but it was unclear how that was happening.
On Friday, Interfax news agency, citing a Russian Defense Ministry spokesman, said Russia had notified the Pentagon it would close down a communication line used to avoid accidental clashes in Syria.
"We have continued to deconflict as necessary with the Russians because whenever we are flying we have to use all the available means to make sure that we don't have any midair incidents.