Trump said he had "no preconditions" for a meeting with the Iranians, adding: "If they want to meet, I'll meet".
Shortly before that July 22 tweet, Mr Rouhani had addressed Mr Trump in a speech, saying that hostile U.S. policies could lead to "the mother of all wars".
Foreign ministry spokesman Bahram Ghasemi on Monday said "there is no possibility for talks", ahead of Trump's statement.
Meanwhile, Iran has rejected Trump's offer to meet and instead has filed a lawsuit against the USA in the International Court of Justice in hopes of blocking United States sanctions set to be reinstated after the U.S. pulled out of the nuclear deal. "I believe in meetings. if they want to meet, we'll meet".
An advisor to President Hassan Rowhani said any talks had to start with Washington returning to the 2015 nuclear deal it abandoned in May.
"I'll meet with anybody", he said.
Trump pulled the US out of a deal with several major powers and Iran earlier this year that was meant to prevent Tehran from developing nuclear weapons.
In the letter, Jafari said Iran never would allow talks with the Great Satan, his label for the US, because the nation's faith in Islam has made it "enormously different from submissive nations".
Iran is less isolated than North Korea and less amenable to a media spectacle that doesn't restore the benefits Iran lost.
Rouhani and some senior military commanders have said Iran could disrupt oil shipments from Gulf states through the Strait of Hormuz if Washington tries to choke off Iranian oil exports. I don't know that they're ready yet.
Thieves steal Swedish royal jewels, escape by speedboat
The other nine are the United Kingdom, Belgium, Denmark, the Netherlands, Norway, Spain, Liechtenstein, Monaco, and Luxembourg. The objects were on display, but under lock and key, at the cathedral about 50 miles from Stockholm .
Midfielder Ramsey unsure of Arsenal future
Gunners fans will get their first glimpses of new signing Sokratis and Lucas Torreira , who both joined the club this summer. Asked how long the negotiations would take, Ramsey replied: "I'm not sure exactly".
"I hope it works out well with Iran".
As a result of Trump's decision to withdraw from the agreement, some previously lifted US sanctions will be reimposed on Iran over the next few months.
Rouhani's chief of staff claimed earlier this month in Iran's state-owned newspaper that Rouhani had rejected eight requests from Trump for one-on-one talks past year.
Washington aims to force Tehran to end its nuclear program and its support of militant groups in the Middle East, where Iran is involved in proxy wars from Yemen to Syria.
It is the first time parliament has summoned Rouhani, who is under pressure from hardline rivals to change his cabinet following a deterioration in relations with the United States and Iran's growing economic difficulties.
Trump, just eight days ago, issued a direct counterthreat to Tehran in an all-capital-letters tweet in which he sharply warned Rouhani to "never threaten the United States" or the Islamic Republic would suffer historical consequences. "How can we trust this country when it withdraws unilaterally from the nuclear deal?"
Monday's olive branch from Trump marks an abrupt shift in tone, and may be little more than theater with United States midterm elections looming on the horizon.
While Iran has lost much of its purchasing capability, Iranian exportation of non-oil related goods is in full swing as foreign buyers are able to get products on the cheap. Trump has long cast himself as a master negotiator who is most effective when he meets with his counterparts face-to-face.
Secretary Pompeo and National Security Advisor John Bolton, in contrast, seem more interested in forcing Iran to capitulate.
In his typical carrot-and-stick approach, Trump exerts increasing pressure on Iran, while leaving the regime a way out.
The jet vanished without a trace on March 8, 2014 with 239 people on board while en-route from Kuala Lumpar to Beijing. He said however he hoped the government would try to find new clues and consider resuming the search.
The explosion happened about 1 p.m. local time just outside the embassy's southeast corner, an embassy spokesman said. Some witnesses claimed that they heard a blast, however, the nature of the explosion is yet to be determined.
The Gunners returned from the break looking like a new team and grabbed an equaliser through youngster Emile Smith Rowe. For me, he's a very good person, a very good professional and he has a lot of experience in the football world.
James Dorsey, an expert on Middle East affairs, said the attacks on oil tankers would draw worldwide attention to Yemen. Oil prices are already high and it is not in the interests of the USA to see them go any higher.
They say they are duty-bound to carry out congressional oversight. "Enough is enough", Jordan said in a statement on Wednesday. Republican leaders, however, have said in recent weeks that they are satisfied with the Justice Department's progress.
Trump formally ended the practice of separating parents from their children when he signed an executive order in June. The alleged victims, Hispanic youths held for months or years, have submitted sworn statements in the case.
Facebook has been an omnipresent part of American news for what seems like all of 2018, and rarely with a positive connotation . Looking ahead, we will continue to invest heavily in security and privacy because we have a responsibility to keep people safe.
Before official results arrived, PTI and Khan supporters took to the streets to celebrate the initial results on Wednesday night. Monitors had been thrown out of polling stations as votes were tallied and results were unexpectedly delayed for hours.
As campaign manager, Manafort was responsible for all aspects of Trump's White House bid, including shoring up delegate support. Mueller's team says Manafort's position in the Trump campaign is relevant to some of the bank fraud charges.
Today, the head of Rinjani national park said 560 people remain on the mountain, although some have started to descend. The powerful quake, whose epicenter was at a depth of 7 kilometers, hit at 6:47 am local time, the USGS said.
Tensions between Assam's indigenous tribes and Bengali-speaking Muslims have led to outbreaks of deadly violence in the past. It was agreed that all foreigners who had entered Assam between 1951 and 1961 would be given full citizenship.
Giuliani: It's time for Mueller to put up or shut up
In an interview on CNN , the former New York City mayor suggested that Trump would have had to pay Russian operatives to collude. Donald Trump has said " collusion is not a crime " ahead of the first trial in the Russian Federation investigation.
Facebook market value plunges $120 bil
Unfortunately, Facebook's spokeswoman declined to release a further comment about the ongoing complaint. Both the slower growth forecast and heavier spending reflect problems largely of Facebook's own making.
New Fortnite Birthday Challenges, New Hero & Free Cosmetics!
This means if you're at 25 health you'll be able to heal fully with the Slurp Juice but won't receive any bonuses to your shield. Epic games seems to have solved this issue this time as well and ensure that there is scope for enough action to go around.