Iranian President Hassan Rouhani will present a plan for creating security in the Gulf in cooperation with other countries in the region when he attends the United Nations General Assembly in NY this week.
Rouhani said the presence of foreign forces in the region would create insecurity for oil and shipping.
Mr Rouhani also said Iran would present a new Gulf peace initiative at the United Nations in the coming days.
Following the attacks, the USA announced that it was sending more troops to the Middle East.
In his speech on Sunday, Rouhani called on the foreign powers in the Gulf region to "stay away".
"If they're honest, then they should not make our region the site of an arms race".
Hassan Rouhani said foreign forces had always brought "pain and misery" and should not be used in an "arms race". "The farther you keep yourselves from our region and our nations, the more security there will be for our region".
"In this sensitive and important historical moment, we announce to our neighbours, that we extend the hand of friendship and brotherhood to them", he said.
The annual military parade marks the start of the week commemorating Iran's 1980-1988 war with Iraq known as the "sacred defence".
The president said it would be presented to the United Nations, which begins the main part of its general assembly in NY on Tuesday.
Following the attacks, which caused global oil prices to spike, Trump initially raised the possibility of a military response, tweeting that the U.S. was "locked and loaded".
President Donald Trump unilaterally withdrew America from the deal over a year ago, and re-imposed crippling sanctions on Iran.
Iran has denied the allegations and said any retaliatory strikes from the USA or Saudi Arabia will lead to "all-out war".
He said: "Wherever the Americans or our enemies have gone ... there has been insecurity afterwards". A domestically built long-range, surface-to-air missile air defense system, the Bavar-373, which Iranian media have described as a competitor to the Russian S-300 missile system, was also on display, according to the semi-official Fars news agency.
The Pentagon announced on Friday that, in response to a Saudi request, there would be a moderate deployment to Saudi Arabia, not in the thousands and focused on air and missile defence.
The attacks had a serious, if not long-term, effect on Saudi oil supplies. Fears of a wider regional conflagration have grown, as tensions between Iran and the United States remain high over Tehran's failing 2015 nuclear deal with world powers.
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