Italian Foreign Minister Angelino Alfano said the USA intervention had offered "a window of opportunity to construct a new positive condition for the political process in Syria".
President Rouhani also condemned the USA -allied Gulf Arab states for supporting the American attack.
He refused to be drawn on whether the United Kingdom would support further U.S. military action in Syria.
Rex Tillerson's first official visit to Russian Federation as secretary of state could not have come at a more awkward time.
Before the statement's release, Iranian President Hassan Rouhani denounced the "flagrant USA aggression on Syria".
President Putin said Russian Federation has intelligence from "trusted sources" that chemical weapons provocations are now being prepared in more regions in Syria, including against Damascus, with the intent to frame Syrian President Bashar al-Assad.
The foreign ministers' discussions will prepare the way for a G7 leaders' summit in Sicily at the end of May, which looks set to be Trump's first overseas trip since becoming president.
Tillerson is traveling Tuesday to Moscow.
"To be clear, our military action was a direct response to the Assad regime's barbarism", Tillerson said at the G7 meeting in Italy.
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U.S. Secretary of State Rex Tillerson steps off his plane at Pisa Military Airport in Pisa, Italy, on Sunday, April 9, 2017.
The two agreed that the USA strike on Syria "changed the course of action by the Assad regime and will lead to a breakthrough in a political process". "They plan to plant some chemical there and accuse the Syrian government of an attack", RT reported Putin said.
USA officials previously have said Russians routinely work with Syrians at the Shayrat air base where the attack is supposed to have originated.
Lavrov also says that Russian President Vladimir Putin could restore a military hotline with the US if Washington focuses on fighting the Islamic State and other extremist groups.
The Trump administration is seeking support from overseas.
He said: "Time and time again Russian Federation has abused its veto to protect the regime and to defend its use of chemical weapons". He says that makes it hard to have clarity about US positions.
The prime minister, who is on a short walking holiday in Wales, has not spoken to Trump since he ordered the firing of 59 cruise missiles at Shayrat airbase, north of Damascus.
Mr Putin's spokesman Dmitry Peskov added that Mr Tillerson would be meeting his Russian counterpart Sergey Lavrov and not the Russian president. It's unclear if Putin and Tillerson will meet.
The results came from analysis of blood and urine samples of the casualties from the attack in Idlib province who were brought to Turkey for treatment.