Cheering crowds have welcomed home the Iranian negotiators who secured a nuclear deal with world powers, while Israel called it a "historic mistake".
US President Barack Obama telephoned Israeli Prime Minister Benjamin Netanyahu, seeking to reassure him of Washington's commitment to Israel.
Sunday's deal in Geneva prompted a fall in oil prices on markets on Monday.
Iran has agreed to curb some of its nuclear activities in return for about $7bn (£4.3bn) in sanctions relief.
Hundreds of cheering supporters greeted Iran's negotiators as they arrived back in Tehran on Sunday, after reaching an interim nuclear agreement with the US, Russia, China, France, the UK, and Germany.
Carrying flowers and Iranian flags at Tehran's Mehrabad airport, they hailed Iran's foreign minister, Mohammed Javad Zarif, as an "ambassador of peace" and chanted, "No to war, sanctions, surrender and insult".
Speaking to Iranian state television at the airport, Mr Zarif said Iran was prepared to take the necessary steps to keep the deal on track. But he said the interim, six-month deal agreed in Geneva could be halted by Tehran at any stage:
"All the measures that we will take, the confidence-building measures, are reversible, and they can be reversed fast. Of course, we hope we don't have to do this."
Sceptical about Iran
Earlier, the US President Barack Obama welcomed the deal, saying it would "help prevent Iran from building a nuclear weapon".
But Mr Netanyahu said Israel would not be bound by the agreement, saying he had a "duty to speak out".
"We cannot and will not allow a regime that calls for the destruction of Israel to obtain the means to achieve this goal."
His comments came as it was revealed that the US and Iran had held a series of face-to-face talks in recent months that paved the way for the agreement but were kept secret even from their allies.
World powers suspect Iran's nuclear programme is secretly aiming at developing a nuclear bomb - a charge Iran has consistently denied.
The deal reached early on Sunday in Geneva will last for six months, while a permanent agreement is sought.
Key points of the deal include:
- Iran will stop enriching uranium beyond 5%, and "neutralise" its stockpile of uranium enriched beyond this point
- Iran will give greater access to inspectors including daily access at the Natanz and Fordo nuclear sites
- There will be no further development of the Arak plant which it is believed could produce plutonium
- In return, there will be no new nuclear-related sanctions for six months if Iran sticks by the accord
- Iran will also receive sanctions relief worth about $7bn (£4.3bn) on sectors including precious metals
The interim agreement with Iran - the world's fourth-largest oil producer - prompted a fall in oil prices in early Asian trading on Monday, with Brent crude falling by more than 2%.
Although Iran will not be allowed to increase its oil sales for six months, analysts say the deal is perceived by the markets as reducing risk in the Middle East.
Earlier, US Secretary of State John Kerry told ABC's This Week programme that the deal was a first step in making sure Iran could not have nuclear weapons.
"Israel will actually gain a larger breathing space in terms of the breakout capacity [to make a nuclear weapon] of Iran," he said.
He added that he hoped Congress would not pass new sanctions but Republican senators - as well as some from President Obama's Democratic party - have expressed concerns about the deal and say more sanctions are possible
In a nationwide broadcast on Sunday, President Rouhani repeated that his country would never seek a nuclear weapon.
"No matter what interpretations are given, Iran's right to enrichment has been recognised," he said.
Tehran insists it must be allowed to enrich uranium to use in power stations.
The deal comes just over three months since Mr Rouhani - regarded as a relative moderate - took office in August, replacing the hardline Mahmoud Ahmadinejad.
It has also been backed by Iran's Supreme Leader Ayatollah Ali Khamenei, who has the final say in nuclear matters.