"In the current context of the withdrawal of the United States. and the intense negotiations between Iran and Europe to find a way to preserve this agreement", the trip "is of prime importance", Iran's foreign ministry spokesman Bahram Ghassemi said Saturday.
He further said "today that there is a new pressure on the Iranian people and society, all Iranians should stand together and increase efforts for the greatness of Iran".
"Despite their radical public approach, hardliners want a compromise with America, but they don't want to give Rouhani the upper hand at home by championing talks", said a source, familiar with Iranian thinking.
After the remarks, US crude jumped more than 8 percent and closed at more than $74 a barrel - a first since November 2014.
To pile on the pain, Washington says all countries must end crude imports from Iran by November 4, hitting the oil sales that generate 60% of the country's income.
Switzerland - where significant parts of the pact known as the Joint Comprehensive Plan of Action were negotiated - will work to ensure that future U.S. sanctions do not target any humanitarian goods, Bern said in a statement.
Federica Mogherini, the EU's foreign relations chief, has said the European Union was determined to protect and deepen key sectors including Iranian energy sales, banking transactions and transportation ties.
Hook said that the first part of U.S. sanctions against Iran will snap back on August 6.
Iran will allow private companies to export crude oil, part of a strategy to counter USA sanctions, and is urging fellow OPEC members, including regional rival Saudi Arabia, not to break output agreements, state media and officials said on Sunday.More news: Trump says Saudi king agrees to ramp up oil production
Donald Trump walks off after delivering a statement on the Iran nuclear deal from the Diplomatic Reception Room of the White House, May 8, 2018.
The top diplomats of Britain, China, France, Germany and Russian Federation will join Iranian Foreign Minister Mohammad Javad Zarif in the Austrian capital, Iran's official IRNA news agency reported, for their first talks together on the deal since Washington pulled out earlier this year.
Meanwhile, a major focus of Trump's campaign is to drive Tehran's economy-sustaining oil exports to zero.
Mr Trump announced on Twitter he spoke to Saudi Arabia's King Salman asking to raise its oil production to take Iran's place on the global market.
Saudi Arabia could cover most of the current Iranian oil supplies for International Olympic Committee if India and its refiners were to cut off Tehran crude intake, Singh said, adding that a narrowing spread between Brent Crude and the Dubai oil benchmark gives refiners more options to source reasonably priced crude oil.
In the previous round of sanctions on Iran's oil, India was one of the few countries that continued to import Iranian oil, albeit at lower volumes because the USA and European sanctions at that time were choking most of the banking, shipping, and insurance processes.
Despite who made the claim - and that the State Department and the Department of Homeland Security have not confirmed it - several news outlets reported the story anyway, which Trump then tweeted.
But so far it has proven hard to offset the impact of continued USA sanctions, with European firms reluctant to risk far-reaching US financial penalties to do business in Iran. In the coming days, he said, he was headed to carry out "very close consultations" Germany, France, and Britain ahead of Trump's anticipated visit.