That prospect alarms Iran's rivals, including Israel and Saudi Arabia, which argue that Tehran is only being emboldened in its quest for regional dominance.
How this plays out depends on whether — for the sake of closer ties with the U.S. and Europe — Iran eventually ends some of the policies that have disturbed the West, such as backing proxy militias in Middle East hotspots. So far, there are no signals from Tehran.
Here's a look at Iran's regional involvement and the potential impact of the nuclear deal.
The Saudi monarchy and other Sunni Muslim rulers in the Arab Gulf are eager to counter Shiite Muslim-led Iran.
The Gulf countries view any normalizing of ties between Tehran and the West as a direct threat to their own stability. Saudi Arabia has accused Iran of funding Shiite rebellions in the Gulf countries of Yemen and Bahrain and whipping up fervor among the kingdom's Shiite minority.
In Syria's civil war, Iran is siding with President Bashar Assad, while Saudi Arabia is backing rebels trying to topple him. Iran has given significant financial support to Assad and is also believed to have sent military advisers to Syria, trained pro-government militiamen and directed one of its proxies, Lebanon's Shiite Muslim Hezbollah group, to fight alongside Assad's troops. Saudi Arabia has sent weapons and money to the rebels, most of them Sunnis.
It's unclear what effect the precedent of successful nuclear negotiations will have on Syria's civil war and on efforts to broker a political resolution to the conflict.
The West acknowledges that Iran is a major player in Syria, but the U.S. and the Syrian rebels remain opposed to Tehran taking part in a proposed peace conference that Washington and Russia are trying to convene.
Assad ally Russia, meanwhile, wants Iran at the negotiating table. It may all be a moot point, since it's unclear whether the peace talks will even take place. Assad's government and the rebels disagree on the ground rules.
Iran and the United States have considerable influence over Shiite and Sunni political groups, respectively, in Iraq. If they were to reach an agreement on Iraq, as they did on the nuclear issue, they could play a major role in defusing sectarian tensions.
Such tensions have been running high, with sectarian attacks, including assaults on Shiite and Sunni mosques, taking place almost daily.
The issue of Iran has loomed in the background of U.S.-mediated negotiations on the terms of a Palestinian state alongside Israel. The talks resumed in late July after a five-year break.
Israel has argued that it cannot take security risks in a deal with the Palestinians because it faces a potential existential threat from Iran. It could now make that point more forcefully, with Prime Minister Benjamin Netanyahu maintaining that the nuclear deal endangers Israel's security.
The nuclear deal has also strained Israel-U.S. ties and might make it more difficult for Washington to exert pressure on Israel on the Palestinian issue, should it decide to do so.
Palestinian negotiators on Sunday praised the nuclear deal as a precedent in which the international community came together to solve a difficult issue. They said the major powers should do the same to try to solve the Israeli-Palestinian conflict that has festered for decades.
However, the U.S. has been unwilling to share its role of mediator with others, and Israel has been staunchly opposed to broader international involvement in the negotiations.
Associated Press writers Karin Laub in the West Bank, Aya Batrawy in Dubai, Sameer N. Yacoub in Baghdad and Ryan Lucas in Beirut contributed to this report.