Sen. Bob Corker (R-Tenn.), with ranking Democrat Robert Menendez (N.J.), speaks during a Senate Foreign Relations Committee hearing on Capitol Hill on March 11, 2015. (Mark Wilson/Getty Images)

Sen. Bob Corker (R-Tenn.), chairman of the Senate Foreign Relations Committee, said Congress must approve any agreement reached by the United States and other world powers to curb Iran's nuclear program.

Corker has proposed a Republican-backed bill to give Congress a critical role in accepting or rejecting a nuclear deal with Iran. It is important that Congress play its "rightful role," he said. The president needs to sell the deal to Congress and the American people, he said.

"There's a lot of water that needs to go under the bridge here. Many, many details are unknown at this point," Corker said.

In an interview on "Fox News Sunday," Corker cited "red flags" in the framework agreement announced last week. One red flag is what elements would be considered before international sanctions on Iran are lifted, he said. Under the current framework, the sanctions would be lifted if Iran meets its commitments.

Corker also said he wanted to see the process that would be in place for the International Atomic Energy Agency to conduct inspections.

[President Obama’s full remarks announcing a ‘framework’ for a nuclear deal with Iran]

The Senate Foreign Relations Committee is scheduled to meet April 14 to vote on the Corker bill. The White House has said that the president would veto the bill, if passed.

President Obama has warned that if Congress jeopardizes the deal, the United States will bear the blame for collapsed international diplomacy. When asked whether he would insist on congressional review, Corker replied, "Absolutely."

Corker acknowledged that Congress would not have an effect on the deal even if it weighs in. But, he said, a congressional review could help ensure that "this deal isn't worse than it is," he said.

"Everyone would say that congressionally mandated sanctions are what helped, in a strong way, get Iran to the table. Certainly, we should approve this deal and we should approve what we see prior to those [sanctions] being lifted," Corker said.

Sen. Dianne Feinstein (Calif.), the top Democrat on the Senate Intelligence Committee, said on CNN's "State of the Union" Sunday that she would not vote for the bill in its current form.

"My understanding is, there may be changes. So I want to be cautious and wait and see what actually comes out of that committee onto the floor before I really cast my vote," Feinstein said.