Iran's president said on Friday that a framework for a nuclear deal was just the first step toward building a new relationship with the world, after his countrymen greeted the announcement of the accord with celebrations in the streets.
US President Barack Obama also hailed an "historic understanding", although diplomats cautioned that hard work lies ahead to strike a final deal.
The tentative agreement, struck on Thursday after eight days of talks in Lausanne, Switzerland, clears the way for a settlement to allay Western fears that Iran could build an atomic bomb, with economic sanctions on Tehran being lifted in return.
In a televised speech on Friday, President Hassan Rouhani, a relative moderate elected in a landslide two years ago on a promise to reduce Iran's isolation, said the nuclear talks were just the start of a broader policy of opening up.
"We are not completely at the end of the road and the end of the road should be in June," said French Foreign Minister Laurent Fabius. "Nothing is signed until everything is signed, but things are going in the right direction."
Netanyahu, who has the ear of Republicans who control both houses of the US Congress, said the powers negotiating with Iran must add a new demand that Tehran recognize Israel's right to exist. Israel believes Iran's goal is to destroy it.
Celebrations erupted in the Iranian capital after the deal was reached. Cars in Tehran honked horns as passengers clapped.
In the weekly sermon at Tehran University, Ayatollah Mohammad Emami-Kashani, a 78-year-old hardline cleric, said Khamenei backed the negotiating team. Emami-Kashani praised the negotiators as "firm, wise and calm" and congratulated Rouhani and Foreign Minister Mohammad Javad Zarif.
Obama described the agreement as an "historic understanding" and compared it with nuclear arms control deals struck by his predecessors - including Republicans - with the Soviet Union that "made our world safer" during the Cold War. He also cautioned, however, that "success is not guaranteed".
With Russia and China joining the United States, Britain, France and Germany as signatories to the deal, and even Iran's Sunni Arab enemies cautiously welcoming it, the only country that was publicly opposed was Israel.
"Israel demands that any final agreement with Iran will include a clear and unambiguous Iranian commitment to Israel's right to exist," Netanyahu said in a statement on Friday.
Germany's Foreign Minister Frank-Walter Steinmeier said it was too early to celebrate. But he also said Israel should study the deal more closely before opposing it.
Global oil prices, which have already fallen sharply in the past year, tumbled on Thursday on the prospect that Iran will eventually be able to restore its exports. Brent crude was off as much as 5 percent at one point before recovering.
France's Fabius said Iran's economy stood to gain $150 billion in relief from the sanctions.
Saudi Arabia's new ruler, King Salman, told Obama by phone on Thursday he hoped a final nuclear settlement would "strengthen the stability and security of the region and the world".