World leaders hailed the Iran nuclear deal on Tuesday, with Barack Obama seeing a "new direction" and Vladimir Putin voicing a global "sigh of relief" -- though Israel criticised it as a "historic mistake".

Major international powers who thrashed out the agreement with Tehran said they hoped Iran would build on the opportunity to come in from the cold.

While Republicans in the United States warned the deal could "embolden" Iran, US President Obama said the agreement offered a chance to reset vexed relations.

"Every pathway to a nuclear weapon is cut off," he said. "This deal offers an opportunity to move in a new direction. We should seize it."

However, Israeli Prime Minister Benjamin Netanyahu called the deal a "historic mistake" marked by "huge compromises" and warned it could still consider pre-emptive strikes against Iranian nuclear sites.

"We did commit to preventing Iran from acquiring nuclear weapons, and this commitment still stands," said Netanyahu, adding that easing sanctions on Iran would "fuel its terror machine".

"Israel is not bound by this deal with Iran because Iran continues to seek our destruction," he said.

Obama reassured the Israeli leader that the deal did not diminish "concerns regarding Iran's support for terrorism and threats toward Israel," according to the White House.

Sealed in Vienna after a 13-year stand-off, the deal was reached between Tehran and the United States, Russia, China, Britain, France and Germany.

Russia's President Putin hailed the deal as a "firm choice for stability and cooperation".

"The world has breathed a huge sigh of relief," he said, pledging that Moscow would "do everything in its power" to ensure the agreement worked.

Russian Foreign Minister Sergei Lavrov said the deal removes "artificial" barriers towards forming a "broad coalition" to fight the Islamic State jihadist group.

The agreement is aimed at ensuring Iran does not obtain a nuclear bomb, in return opening up Tehran's sanctions-stricken economy.

Iran has always denied Western accusations that its civil nuclear programme was a cover for acquiring nuclear weapons.

- Saudi hopes -

Saudi Arabia expressed hope Tuesday for an end to Iran's regional "interference", while two of the kingdom's fellow Sunni-run Gulf neighbours also expressed hope for improved relations with Shiite-dominated Iran.

"Iran should, with the conclusion of this accord, put her resources towards its development and amelioration of the condition of the Iranian people instead of provoking troubles which would generate certain reactions from countries in the region," said an official spokesman cited by the Saudi Press Agency.

A United Arab Emirates official said Iran could play a significant regional role if it "stops interfering in the internal affairs of countries like Iraq, Syria, Lebanon and Yemen".

Kuwait's emir, Sheikh Sabah al-Ahmad al-Sabah, hoped the deal would help to "direct all efforts for the development" of the region.

United Nations Secretary General Ban Ki-moon said the agreement "could serve as a vital contribution to peace and stability both in the region and beyond".

Spain, which presides over the UN Iran sanctions committee, said it would ensure the proper implementation of the agreement and hoped it would facilitate Iran's reintegration into the international community.

NATO called it a "historic breakthrough" that would strengthen global security, but said it was "critical" for Tehran to comply with the terms of the accord.

British Prime Minister David Cameron said the deal would help "make our world a safer place" and said Iran now had a "real opportunity" to benefit from the pact economically.

German Chancellor Angela Merkel hailed it as "an important success" of international diplomacy, and Vice Chancellor and Economy Minister Sigmar Gabriel now plans to visit Iran soon.

- Region welcomes agreement -

French President Francois Hollande said "the world is making headway," urging Tehran to help world powers end the Syrian conflict.

Syria's President Bashar al-Assad said his key ally Iran had "achieved a historic victory", while Egypt said it hoped the deal would "prevent an arms race in the Middle East".

Iran's neighbour Afghanistan said it welcomed efforts aimed at "strengthening of peace and stability in the region", while Pakistan said that confidence-building measures over Tehran's nuclear programme "auger well" for regional security.

Turkish Foreign Minister Mevlut Cavusoglu said the deal would boost the regional economy, while his Iraqi counterpart Ibrahim al-Jaafari said the agreement must "be implemented for the region to reach stability".

In South America, both Brazil and Argentina expressed "satisfaction" with the deal, with the Brazil government expressing hope it could contribute to "the beginning of a new productive phase in relations between Iran and other parties".

Meanwhile the Vatican hoped the agreement would "bear fruit" which would extend beyond simply Iran's nuclear programme.

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