"There is no good argument for us to try to undercut, undermine the negotiations until they`ve played themselves out," Obama told reporters.
"Congress needs to show patience," he added. "My main message to Congress is: `Just hold your fire.`"
Obama said he told Democratic lawmakers he would veto a bill calling for new sanctions if it landed on his desk.
The joint push with Cameron, who said he had personally called U.S. senators about the issue, represented the strongest effort yet by the White House to prevent U.S. lawmakers from both parties from seeking to force additional penalties on Tehran.
The United States, Britain, France, Germany, Russia and China are in talks with Iran to forge a deal over Tehran`s nuclear program. They failed to meet a self-imposed deadline for a solution in November. Obama put the chances of an eventual deal at 50/50.
But the president warned that if the Congress forced further sanctions, Iran could use that as an excuse to abandon the talks and accuse Washington of blowing up the deal and acting in bad faith.
"There would be some sympathy to that view around the world, which means that the sanctions that we have in place now would potentially fray," Obama said.
"Congress should be aware that if this diplomatic solution fails, then the risks and likelihood that this ends up being, at some point, a military confrontation is heightened. And Congress will have to own that as well."
He clarified, however, that if a deal did not emerge, that did not mean Washington would shift toward a military posture.
"I am not, repeat not, suggesting that we are on immediate war footing should negotiations with Iran fail," he noted. "The bottom line is this: We may not get there, but we have a chance to resolve the nuclear issue peacefully."
Republican and Democratic lawmakers are moving forward with a new sanctions bill, and some expressed offense at Obama`s remarks.
"Iran is a state sponsor of terror with an abysmal human rights record, and yet President Obama is so committed to his negotiations with this regime that he is vowing to veto tougher sanctions," House Speaker John Boehner said in a statement.
"No White House threat will stop us from doing the right thing to protect the United States and its allies."
The Senate Banking Committee plans to debate and vote on the bill on Thursday.
U.S. Secretary of State John Kerry and Iranian Foreign Minister Mohammad Javad Zarif met in Paris on Friday to try to iron out disagreements over Iran`s nuclear program, which Tehran says is peaceful.
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