By Aresu Eqbali in Tehran and Asa Fitch in Dubai 

Iran celebrated the removal of economic sanctions on Sunday, even as regional rivals warned that it was still out to destabilize the Middle East and needed to be closely monitored.

Western officials said the implementation of Iran's nuclear deal with six world powers, which allowed for the lifting of some economic sanctions, raised prospects for overhauls within Iran's political system. The deal has been a priority for President Hassan Rouhani, a relative moderate in the conservative clerical regime who was elected on a platform of engagement with the world in 2013.

Mr. Rouhani hailed the implementation of the deal, saying this had turned a "golden page" in the country's history and heralded an economic revival.

"Conditions will be better than before for political and economic relations with regional countries, and we can resolve regional problems, " Mr. Rouhani said in a televised news conference, pointing to hope that the deal would create an atmosphere of reconciliation in the region.

But Israeli Prime Minister Benjamin Netanyahu said on Sunday that his country would continue to monitor Iran's behavior closely.

"Even after the signing of the nuclear agreement, Iran has not relinquished its aspiration to obtain nuclear weapons and it will continue to undermine stability in the Middle East and spread terrorism around the world while violating its international obligations," a statement from Mr. Netanyahu's office said.

In Saudi Arabia, there was concern that the lifting of sanctions would bolster Iran and its allies. A statement by 140 Sunni Muslim clerics urged Muslims to unite against the threat of Shiite Iran. It criticized actions by some minority groups in Muslim countries and accused them of "serving foreign agendas," a veiled reference to what they view as the loyalty of Shiites in Sunni-majority Arab countries to Iran.

Iran's rivals are also worried that Tehran will spend some of the billions of dollars of oil revenue unfrozen by the lifting of sanctions on aiding regional allies that include Syrian President Bashar al-Assad, the Shiite group Hezbollah in Lebanon and the Shiite-linked Houthi rebels in Yemen.

Iran's central bank governor, Valiollah Seif, estimated these funds at $32.6 billion on Sunday. But Treasury Secretary Jack Lew estimated last July that Iran would have access to about $50 billion after sanctions relief.

Mr. Seif said on Saturday that bringing the funds back to Iran would be unreasonable, adding they would likely be used to purchase imports, the official Islamic Republic News Agency reported. In his speech on Sunday, Mr. Rouhani only said the money "will be at the disposal of our people for economic activities."

Mr. Seif and other Iranian officials such as Foreign Minister Javad Zarif held up the sanctions relief as a catalyst for investment in Iran and for future cooperation in the fight against terrorism.

Parliamentary elections in February are expected to serve as a referendum on public acceptance of Mr. Rouhani's pursuit of better ties with the world.

"Rouhani and Zarif were the responsible architects, if you will, on the Iranian side, of the nuclear agreement," said Peter Wittig, the German ambassador to the U.S. "We hope that they will garner some support because of the sanctions relief."

Tensions between Saudi Arabia and Iran rose recently with a series of events that began with the Saudi execution of prominent Shiite cleric and activist Nemer al-Nemer on Jan. 2. Angry Iranians responded by storming Saudi diplomatic complexes in Tehran and Mashhad, Iran's second-largest city.

Iranian leaders condemned the attacks on Saudi diplomatic compounds. But the kingdom cut off diplomatic and commercial ties with Iran on Jan. 3. A host of Sunni Saudi allies followed by downgrading or severing diplomatic ties with Tehran.

Saudi Arabia has been leading a coalition of Sunni countries battling the Houthis in Yemen since last March.

The rise in Saudi-Iranian tensions coincided with a thaw in relations between the U.S. and Iran. The U.S. along with the U.K., France, Germany, Russia and China reached the nuclear deal with Iran in July. Under it, Iran agreed to curtail its nuclear activity in exchange for relief from the sanctions that have crippled its economy.

The latest sign of improvement in U.S.-Iranian relations in the aftermath of the nuclear deal came Saturday when the countries agreed to a rare prisoner swap. Four Americans held by Iran were released and three of them left the country on Sunday, including Washington Post correspondent Jason Rezaian.

President Barack Obama on Sunday said the release of the imprisoned Americans and Iran's completion of steps to curtail its nuclear program mark clear victories for his diplomacy-first foreign-policy doctrine.

Mr. Obama said he hopes the moves lead to more cooperation between the U.S. and Iran going forward. At the same time, amid criticism that Iran receives a financial windfall under the terms of the deal, he announced new sanctions against Tehran targeting its ballistic-missile program.

Ibrahim Fraihat, a senior foreign-policy fellow at the Brookings Institution in Qatar, said a significant slice of the money unfrozen by eased sanctions would likely go toward rebuilding the domestic economy.

Iran's economy shrunk in 2012 and 2013 because of sanctions, according to International Monetary Fund figures, and Mr. Rouhani has stressed the need for investment in local industry and infrastructure to reach a government target of 8% annual GDP growth.

Iranian leaders must also satisfy a public that wants to see tangible economic dividends from sanctions relief, Mr. Fraihat said. A poll conducted last year by IranPoll.com and the University of Maryland found that 62% of Iranians expected to see a tangible improvement in living standards within a year of the deal.

"We have to keep in mind that Iran is under tremendous economic pressure to deliver internally," Mr. Fraihat said.

Ahmed Al Omran in Riyadh, Saudi Arabia, and Felicia Schwartz in Washington contributed to this article.

Write to Asa Fitch at asa.fitch@wsj.com

(END) Dow Jones Newswires

January 17, 2016 14:46 ET (19:46 GMT)