By Carol E. Lee And Jay Solomon 

WASHINGTON--President Barack Obama suggested on Friday that Iran could receive significant economic relief immediately after concluding a deal to curb its nuclear program, a gesture towards one of Tehran's key demands.

Mr. Obama said such a move would depend on the final accord allowing international sanctions to be quickly re-imposed if Tehran violated the agreement it is now negotiating with global powers. The administration has said the U.S. prefers sanctions would be lifted in phases as Iran meets certain requirements.

"Our main concern here is making sure that if Iran doesn't abide by its agreement that we don't have to jump through a whole bunch of hoops in order to reinstate sanctions," the president said at a news conference. "It will require some creative negotiations," Mr. Obama said, adding, "I'm confident it will be successful."

Such solutions could potentially include a faster timetable for lifting sanctions and also freeing up tens of billions of dollars in Iranian oil revenue that has been frozen, though Mr. Obama made no reference to that money.

Later, seeking to clarify the president's comments, a White House official said Mr. Obama "will not accept a deal without phased sanctions" relief.

How sanctions would be lifted under is becoming a flashpoint as Iran and the West try to move from a preliminary agreement made earlier this month to a final deal by a June 30 deadline.

Mr. Obama, at the news conference, which came after meeting with Italian Prime Minister Matteo Renzi, said the level and timing of sanctions relief are less important to the U.S. than the measures that will determine how quickly sanctions can be re-enacted if Iran breaks any final agreement.

On both the lifting of sanctions and the "snap back" provisions that put them back in place if Iran is in violation, Mr. Obama said U.S. negotiators will be seeking "formulas that get to our main concerns while allowing the other side to make a presentation to their body politic that is more acceptable."

The president's comments follows defiant statements from Iran's leaders over the past week insisting that a final agreement lift sanctions immediately. Mr. Obama appeared to offer a roadmap for satisfying demands by both Iran and U.S. lawmakers who are skeptical over the talks.

In Iran's ongoing talks with the U.S., the U.K, France, Germany, China and Russia, the structuring of sanctions relief, as well as the provisions for inspecting Iran's nuclear infrastructure, was left unclear in the framework agreement.

Opponents of the Iran deal on Capitol Hill have become increasingly concerned that the White House could soften its position in response to Iranian demands, a fear exacerbated by the president's comment.

"Throughout the negotiations, we've lost ground, and Iran in every step of this negotiation has gained ground," said the chairman of the House Foreign Affairs Committee, Rep. Ed Royce (R., Calif), in an interview on Friday. "The idea that they will have snap backs...is not a credible argument."

U.S. allies in the region, particularly Israel, Saudi Arabia and the United Arab Emirates, have voiced concern that Iran will use any economic windfall to strengthen its regional influence.

The Obama administration estimates Iran has between $100 billion and $140 billion of its oil revenue frozen in offshore accounts as a result of sanctions. U.S. officials said they expect Tehran to gain access to these funds in phases as part of a final deal. Iran could receive somewhere between $30 billion and $50 billion upon signing the agreement, said congressional officials briefed by the administration.

Complicating negotiations, U.S.-ally Saudi Arabia has repeatedly charged in recent weeks that Iran has provided significant funding, arms and training to Shiite insurgents in Yemen who gained control of the country's capital, San'a, and forced the country's president to flee. Iran has denied these allegations. Iran also is a major supporter of the Lebanese militia Hezbollah, the Assad regime in Syria and a group of Shiite militias fighting in Iraq.

"The Iranians, last time I checked, did not have a border with Yemen," Saudi Arabia's ambassador to Washington, Adel al-Jubeir said this past week. "There is no reason for Iran to be involved. There is no reason for Iran to be supporting one faction against the other."