Congress expressed bipartisan concern Sunday about the deal the United States and allies reached overnight with Iran to halt that country’s nuclear program.

“My greatest concerns are seeing follow-through,” Tennessee Sen. Bob Corker, the top Republican on the Senate Foreign Relations Committee, told “Fox News Sunday.” “This administration is very big on announcements and less so on following through. [Iran] is spiking the ball in the end zone.”

He also repeatedly said he didn’t want the interim deal to “become the norm.”

Corker was joined on the show by Sen. Ben Cardin, D-Md., also a member of the chamber’s foreign relations committee.

“We are very concerned as to whether Iran will live up to these agreements,” Cardin said. “Congress needs to be prepared.”

Both suggested that Capitol Hill is prepared to reinstate sanctions that have been lifted in the deal and impose new ones.

Iran and six world powers reached a deal early Sunday that would halt parts of Iran’s nuclear program in exchange for what was described by the Obama administration as “modest relief” from international sanctions.

Obama, speaking from the White House while Secretary of State John Kerry helped ink the agreement in Geneva, called it a “first step toward a comprehensive solution."

The deal, while historic, is a six-month agreement. Republican senators in Washington warned shortly after the terms were announced that Western powers were giving up too much in exchange for too little, in hopes of a longer-term deal. Sen. Mark Kirk, R-Ill., said it would give a leading sponsor of terror "billions of dollars in exchange for cosmetic concessions."

Sen. Marco Rubio, R-Fla., said that the agreement "makes a nuclear Iran more, not less, likely," and called the deal "a blow to our allies in the region who are already concerned about America's commitment to their security and it sends the wrong message to the Iranian people, who continue to suffer under the repressive rule of their leaders who have only their own self-preservation in mind."

But Obama insisted the sanctions relief is reversible if Iran doesn’t live up to its end of the bargain.

"The broader architecture of sanctions will remain in place and we will continue to enforce them vigorously," said Obama, who urged Congress not to pass new sanctions against Iran in light of the agreement, saying "doing so would derail this promising first step, alienate us from our allies, and risk unraveling the coalition that enabled our sanctions to be enforced in the first place."

Under the terms of the agreement, which concluded days of negotiations in Geneva, Iran committed to halt enrichment above a 5 percent threshold and dismantle the technical connections required to enrich uranium above that threshold.

Iran is also required to neutralize its stockpile of near 20 percent enriched uranium, and halt progress on its enrichment capacity. In return, the six world powers (the U.S., Great Britain, France, Germany, China and Russia), have agreed to not impose any new sanctions, suspend sanctions on certain sectors of Iran's economy, and potentially unfreeze $4.2 billion in revenue from oil sales if Iran meets other conditions.

A White House statement also said Iran's nuclear program will be subject to "increased transparency and intrusive monitoring."

Speaking from the White House late Saturday night, Obama said that the terms of the deal were "substantial limitations which will help prevent Iran from building a nuclear weapon. Simply put, they cut off Iran’s most likely paths to a bomb."

However, Obama warned that sanctions relief was dependent on Iran living up to its end of the agreement, saying, "In these negotiations, nothing will be agreed to until everything is agreed to. The burden is on Iran to prove to the world that its nuclear program will be for exclusively peaceful purposes."

Iran President Hassan Rouhani endorsed the agreement in a nationally broadcast speech Sunday, saying the accord recognizes Iran's "nuclear rights" even if that precise language was kept from the final document because of Western resistance.

"No matter what interpretations are given, Iran's right to enrichment has been recognized," said Rouhani, who later posed with family members of nuclear scientists murdered in recent years whose killings Iran has blamed on Israel and its allies.

Saying "trust is a two-way street," Rouhani insisted that talks on a comprehensive agreement should start immediately.

Iranian Foreign Minister Mohammad Javad Zarif, who led his country's delegation, called on both sides to see the agreement as an "opportunity to end an unnecessary crisis and open new horizons."

But reaction in Israel was strongly negative. Israeli Prime Minister Benjamin Nentanyahu called the deal "a historic mistake" in remarks to his cabinet Sunday. Earlier in the day, Intelligence Minister Yuval Steinitz, who is responsible for monitoring Iran's nuclear program, said the deal was based on "Iranian deception and self-delusion."

In an interview on Israel Defense Forces radio, Israel’s Finance Minister, Yair Lapid, sounded a bitter tone.

“We had a choice here between the plague and cholera," Lapid said, according to the website algemeiner,com. We were left alone explaining the truth, and all of our options were bad,” he said. “I don’t understand how the French Foreign Minister can call an agreement that doesn’t involve the dismantling of one centrifuge a ‘victory.’ I can’t understand the world’s failure to notice the nineteen thousand Iranian centrifuges Obviously a deal is better than a war, but not this deal. Netanyahu did everything he could and we all stand behind him on this”

The deal came after the personal intervention by Kerry and other foreign ministers whose presence had raised hopes for a breakthrough.

"The purpose of this is simple," said Kerry, who spoke early Sunday morning, Geneva time. "Requiring Iran to prove the peaceful nature of its nuclear program and prove it does not have a nuclear weapon.

"It will make our partners in the region safe. It will make Israel safer."

"Agreement in Geneva," Kerry had tweeted. "First step makes world safer. More work now."

The deal marks a milestone between the two countries, which broke diplomatic ties 34 years ago when Iran's Islamic revolution climaxed in the storming of the U.S. Embassy in Tehran. Since then, relations between the two countries had been frigid to hostile.

Although the deal lowered tensions between the two countries, friction points remain -- notably Iran's support of the Syrian regime of Bashar Assad. The United States also has said Iran supports terrorism throughout the region and commits widespread human rights violations.

Since it was revealed in 2003, Iran's enrichment program has grown from a few dozen enriching centrifuges to more than 18,000 installed and more than 10,000 operating. The machines have produced tons of low-enriched uranium, which can be turned into weapons grade material.

Iran also has stockpiled almost 440 pounds of higher-enriched uranium in a form that can be converted more quickly to fissile warhead material than the low-enriched uranium. Its supply is nearly enough for one bomb.

The Associated Press contributed to this report.