The signing of a short-term nuclear accord between Iran and six world powers on Sunday left ardent critics of the Islamic republic — most vocally the Israeli government and many U.S. lawmakers — deeply worried that the Obama administration and its partners were making a historic mistake.

“Today the world has become a much more dangerous place, because the most dangerous regime in the world has taken a significant step toward attaining the most dangerous weapon in the world,” Israeli Prime Minister Benjamin Netanyahu said.

He vowed to spend the six months covered by the interim agreement pushing the White House and other allies for a long-term deal that not only curbs Iran’s current nuclear program but also dismantles the infrastructure that could allow it to make a nuclear device. In Congress, many Republicans and some influential Democrats echoed Israeli concerns that the deal freezes Iran’s uranium enrichment but does not reduce its capacity. Tehran says the enrichment is for energy, not weapons production, but many U.S. lawmakers and critics in the international community are skeptical of that claim.

“In my view, this agreement did not proportionately reduce Iran’s nuclear program,” Senate Foreign Relations Committee Chairman Robert Menendez (D-N.J.) said in a statement. “Given Iran’s history of duplicity,” he added, enforcement of the deal “will demand ongoing, on-the-ground verification.”

Saudi Arabia and other Persian Gulf states, which had allied themselves with Israel’s position in opposing the proposed deal, were muted in their reactions Sunday.

The ruling family in Riyadh — already at odds with the Obama administration over Syria policy and other issues — had no official comment. The United Arab Emirates’ state news agency said its government “hopes this would represent a step towards a permanent agreement that preserves the stability of the region and shields it from tension and the danger of nuclear proliferation.”

Most Israeli politicians, from across the political spectrum, say a final deal to lift economic sanctions must require Iran to dismantle its centrifuges, remove its enriched uranium and decommission its heavy-water reactor in Arak, among other things. While Israel is clearly unhappy with the interim deal, some Israeli politicians emphasized on Sunday that their country must accept it as reality, and work to repair the diplomatic fissures that have erupted between Israel and its allies in order to retain influence going forward.

Finance Minister Yair Lapid, a centrist and the second-most powerful politician in Netanyahu’s coalition government, told Israeli Army Radio he was worried not only about what he agreed was a “bad deal,” but “also because we have lost the ability to make the world listen.”

“Our job is to be the ones to warn,” Lapid said. “We need to make the Americans to listen to us like they have listened in the past.”

Labor Party leader Isaac Herzog said Netanyahu “must do everything in order to fix the damage that was caused from the public clash with the U.S., and return to an intimate relationship with President Obama and other world leaders.”

Obama has argued that diplomacy must be tried before a military strike is considered. The president spoke by telephone with ­Netanyahu on Sunday, reiterating that the United States shares Israel’s goal of preventing Iran from obtaining a nuclear weapon, and enlisting Netanyahu’s cooperation as negotiations continue.

At the heart of the concerns about the interim agreement is a belief that the deal has, in effect, frozen in place an advanced uranium-enrichment regimen and allowed a plutonium production reactor to remain on standby, in return for the economic relief that the Iranian government is urgently seeking.

“It does not seem proportional,” said Sen. Charles E. Schumer (D-N.Y.), the Senate’s third-ranking Democrat. “Iran simply freezes its nuclear capabilities, while we reduce the sanctions. . . . A fairer agreement would have coupled a reduction in sanctions with a proportionate reduction in Iranian nuclear capability.”

Some skeptics also say that Obama, eager for a foreign policy achievement, may be too willing to allow Iran to preserve its current enrichment program beyond the six months covered by the interim deal.

Israel defends its vociferous campaign against the agreement by pointing out that Israel is the object of Iranian taunts, and saying that a nuclear Iran is not only a geopolitical challenge for Israel, but poses an existential threat. The most recent proof, officials say, are comments last week by Ayatollah Ali Khamenei, the supreme leader of Iran, who referred to Israel as “the rabid dog of the region” and promised that “the Zionist regime is doomed to destruction.”

“This is the real Iran. We are not confused,” Netanyahu said last week.

Iran says that its nuclear program is peaceful and that it has a right to enrich uranium, as other nations do. While Iran has put in place elements of a military program, U.S. officials say Iran has not made the decision to move ahead with a nuclear weapon.

Netanyahu stressed Sunday that Israel was not a party to the interim agreement and would do what it felt was necessary to keep Iran from obtaining a nuclear weapon. Foreign Minister Avigdor Lieberman, asked whether the interim deal might lead to a military strike by Israel, ominously declined to rule the option out.

“This brings us to a new reality in the whole Middle East, including the Saudis. This isn’t just our worry,” Lieberman told Israel Radio. He called the interim agreement “the biggest diplomatic victory Iran has had in years. . . . We’ve found ourselves in a completely new situation.”

Wilson reported from Washington. Ruth Eglash in Jerusalem contributed to this report.