Tehran and Washington have been at loggerheads since the United States previous year withdrew from a 2015 global deal between Iran and world powers under which Iran agreed to rein in its nuclear activities in return for an easing of sanctions.
"Our response to talks under pressure is 'No, '" Rouhani said in a speech to the General Assembly even as the United States increased the pressure by sanctioning Chinese firms for dealing in Iranian oil despite USA sanctions.
On Wednesday, the U.S. Treasury announced new Iran-related sanctions on five Chinese individuals and six entities it accuses of knowingly transferring oil from Iran in violation of Washington's curbs on Tehran.
In a departure from previous United Kingdom policy, Mr Johnson also criticised the Iran nuclear deal - under which Iran agreed to limit its sensitive nuclear activities in return for the lifting of economic sanctions.
Under the 2015 deal, Iran limited its nuclear programme in return for relief from economic sanctions that constricted its ability to trade with the world.
German Foreign Minister Heiko Maas said that there had at least been progress in moving toward diplomacy.
Tensions between Iran and the USA have been escalating for more than a year since Trump withdrew the US from the 2015 Iran nuclear deal, after which the U.S.re-imposed economic sanctions on the Islamic Republic.
While the USA president has not ruled out meeting with Iranian President Hassan Rowhani, who will address the assembly on Wednesday, the chance of that happening seems unlikely. They should return to the JCPOA, lift sanctions and end this unfair maximum pressure on Iran. He pressed Rouhani and told him it's "now time for them to move if they want to go forward, to have less sanctions and go for a deal", the diplomat told ABC News.
Iran has dismissed any prospect of talks with US President Donald Trump on the sidelines of the ongoing 74th UN General Assembly (UNGA) in NY until Washington stops its campaign of "maximum pressure" on Tehran.
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"President Trump asked me that if we could de-escalate the situation and maybe come up with another deal".
"We must create mutual trust", Rouhani said.
"But no I haven t spoken - he actually asked me, he thought it would be a good idea to meet and we re here, we re in NY together and we have the time to do it, although we ve done a lot of bilats in the last two days".
In retaliation, Iran has gradually reduced its commitments to the agreement.
He stressed that the JCPOA was the best agreement that could be reached, adding that in its reports, the International Atomic Energy Agency has repeatedly confirmed Iran's compliance with its obligations under the accord.
Later in the day, Trump told reporters that Iran "would like to negotiate. I'm hoping there'll be a Trump deal", added the top minister.
"In the event of an incident, you and we shall not remain alone".
Rouhani used his speech at the United Nations to invite Gulf countries to join what he termed the "Coalition of HOPE", which he said stands for the Hormuz peace endeavor.
Yemen's Iran-backed Shi'ite Huthi rebels have claimed responsibility for the drone and missile attack, and Tehran denies any involvement.