Sen. Lindsey Graham (R-S.C.) said adding the language would "send an appropriate" signal to Iran but would not be intended to green-light military action but, instead, to restate U.S. policy.
"I just want to add one simple line that says we recognize what the president was saying that military force is also an option," Graham said on the floor during a debate over the current version of the bill.
"The problem I have is that it is silent on a concept that we all agree on and I don't want to create a document before negotiations on Tuesday that doesn't include something beyond sanctions to change the Iranian behavior we all want to avoid," he said.
Sen. John McCain (Ariz.), the top Republican on the Senate Armed Services Committee, said adding the language should not be a problem because it does not represent a major change in policy toward Iran.
Republicans agreed that, in its current form, the bill would back away from Obama's tougher policy that he would do anything necessary to stop Iran from acquiring nuclear weapons capability.
"It echoes the policy of the country, not just sanctions and we'll get a lot of votes for this," Graham said.
Sen. Joe Lieberman (ID-Conn.) who has sponsored a separate use of force resolution with Graham and Sen. Bob Casey (D-Pa.), said lawmakers should be able to reach agreement sometime Thursday on any additional language.
Regardless, passage of the bill would still require the president to ask Congress for any use of force in the region, if needed, he said.
Still, Sen. Bob Menendez (D-N.J.) urged Republicans not to stall the bill over the language although he shared concerns that the Senate should be on record that Iran cannot be allowed to obtain nuclear weapons, especially before next week's nuclear talks in Baghdad between Iran and the P5+1 group, the five permanent U.N. Security Council members plus Germany.
He said they should pass the Lieberman-Graham-Casey resolution separately and in tandem with the economic sanctions bill.
"You should not hold hostage the sanctions legislation in order to push a goal that should be taken care of by the Lieberman-Graham resolution," he said.
The resolution states that it is unacceptable to contain a nuclear-armed Iran and is intended to send a message to the Iranians that U.S. will do whatever is necessary to stop them from acquiring a nuclear-weapons capability.
Tehran reportedly wants the sanctions lifted as the second round of nuclear talks get under way, as the Obama administration has credited the pressure from sanctions for bringing Iran back to the negotiating table.
Menendez said that previously no one sought to include a "use of force" provision and the change in the bill, reiterating that it does not constitute a declaration of war, was added to appease Republicans.
Negotiators added language by Sen. Rank Paul (R-Ky.) noting that this bill is not an authorization of use of military force, even though Graham and McCain said the provision isn't needed and felt it weakened the measure.
Senate Majority Leader Harry Reid (D-Nev.) expressed frustration after going to the floor with the intention of getting enough support to pass the measure, which has languished in talks since the Senate Banking panel unanimously approved the bill in February.
But Senate Minority Whip Jon Kyl (R-Ariz.) objected, asking Reid for more time over the weekend to work out final language.
"I would hope that we could just have some time over the weekend and perhaps on Monday when enough of the members can be apprised of what has actually been proposed here and see if our colleagues on the other side would be willing to make the accommodation we may need to have made here," Kyl said on the floor.
Reid pushed back against Senate Republican Leader Mitch McConnell (Ky.) and other Republicans saying that they didn't have enough time to look at the bill.
"The language they're objecting to is in the base-bill," Reid said.
"So unless they didn't read the base-bill, we have a problem here," Reid said.
"Mr. President this has been a classic example of rope-a-dope."
Reid said work on the legislation had been going on for two months and that the language Republicans were objecting to was in the original bill. He added that McConnell had a draft of the bill he was trying to move on Wednesday.
"Two months ago I came to the Senate floor and said we need to pass the sanctions immediately," Reid said. "I work more than five days a week and I have been working the last two months trying to get this done."
The legislation includes part of an amendment that Sen. Mark Kirk (R-Ill.) aimed at strengthening sanctions "against companies that engage in or support censorship in Iran.
The bill also includes an amendment Menendez on Iran’s jamming of satellite communications.
In addition, the agreement includes non-binding language recommending intensified sanctions enforcement and monitoring of sanctions evasion efforts by Iran, and urging President Obama to further study the other areas of concern raised by Kirk.
Reid previously tried to pass similar legislation by unanimous consent in late March.
The agreement also includes additional changes strengthening human rights provisions, recognizing the European Union’s recent cut-off of designated Iranian banks from the Society for Worldwide Interbank Financial Telecommunication (SWIFT), which is used to move money around the world, and refining provisions related to victims of terrorism in Iran, a Democratic aide said.
The improved package has the backing of the American Israel Public Affairs Committee (AIPAC), a pro-Israel lobbying group, which sent a letter to lawmakers on Thursday urging support for the measure.
House Foreign Affairs Committee Chairman Ileana Ros-Lehtinen (R-Fla.) expressed concern Thursday about the direction the bill is taking.
“I am deeply concerned that the administration’s foolish embrace of yet another round of negotiations will only embolden the regime," she said at a hearing.
"The administration has made concession after concession in its negotiations with Iran only to come empty handed.
"The Iranian approach seems to be: 'What's mine is mine, and what's yours is negotiable.'"
Iran has argued that its nuclear program would be used for civilian, mostly energy, purposes whereas U.S. officials have argued that the nation wants to build weapons.
The House passed its version of the measure in December and passage in the Senate would require lawmakers to agree on a final bill.