"In this regard, we are even ready to forgive their past mistakes, because today we are faced with conditions in which the enemies of the region, particularly the United States, the arrogance and the Zionism, are seeking to exploit the gap, rift, and division among the regional countries", the president said.
Under the plan, dubbed the Hormuz Peace Endeavor, or HOPE, he said, "all the coastal states of the Persian Gulf are invited to join this coalition to provide and maintain regional security".
"Foreign forces can cause problems and insecurity for our people and for our region", said Rouhani, who will travel to NY later this week for the annual gathering of world leaders at the UN.
Iran has denied any involvement.
Mr Johnson gave the first attribution of blame from the United Kingdom before landing in the U.S. in the early hours of Monday.
In his speech, Rouhani called on the foreign powers in the Gulf region to "stay away", adding: "If they're honest, then they should not make our region the site of an arms race".
In recent weeks, Trump had weighed the possibility of easing sanctions on Iran and suggested he could meet with Iranian President Hassan Rouhani, who is due to attend the U.N. General Assembly in NY this week.
Rouhani's visa was issued, however, with limited and restricted travel restrictions - the Iranian president can only travel between his place of accommodations in Manhattan, the United Nations headquarters and the Iranian embassy.
Rouhani said he would present an Iranian plan for peace in the Gulf to the UN General Assembly.
France has led a European effort to try and defuse tensions between Washington and Tehran but those efforts have stalled, with Iran reducing its commitments to a 2015 nuclear deal with world powers and the United States refusing to ease sanctions that have strangled Iran's economy.
While Yemen's Iranian-allied Houthi rebels claimed the assault, Saudi Arabia says it was "unquestionably sponsored by Iran".
"When the Americans aren't willing [to let Iran participate], we must insist on traveling", Rouhani said.
"The UK is attributing responsibility with a very high degree of probability to Iran for the Aramco attacks".
"It is clear that they would like to completely take hold of eastern Saudi Arabia's oil", he said.
Numerous sanctions had applied before Tehran's 2015 nuclear deal with world powers promised to lift them, in exchange for curbing the country's atomic program.
Iran denies being responsible and has warned any retaliatory attack targeting it will result in an "all-out war".
"This means the U.S.is completely desperate", he said, suggesting the US had little leverage left over Iran.