"There is no good argument for us to undercut, undermine the negotiations until they play out," Obama said.
Obama said hitting Iran's economy with new sanctions in the next 60 to 90 days would violate an interim agreement reached last year, deepen recriminations, and heighten the risk of a military confrontation.
"Congress needs to show patience," Obama said.
If a deal is not reached, with assurances that Iran could not obtain a nuclear weapon, "I would be the first one to come to Congress to say we need to tighten the screws," he added.
Republicans and Democrats in Congress are pushing for another immediate round of sanctions on the Iranian economy, a move led by some high-profile White House allies.
While the gathering was closed to reporters, Menendez was said to have taken “personal offense” to Obama’s suggestion that the legislation was politically-motivated, sources told the New York Times.
Obama said today that the chances of a deal with Iran are “likely less than 50-50" -- but argued the talks are the best chance in decades of resolving the nuclear standoff.
Prime Minister Cameron also warned Congress against new sanctions and said he would personally call lawmakers to express the UK view.
"I have contacted a couple senators this morning, and I may speak to a few more this afternoon," he said, "simply to make the point that as a country that stands along side America in these vital negotiations that its our opinion that further sanctions won't help."
The major western powers and Iran have given themselves until late June to reach a comprehensive agreement that would ultimately rescind tough western sanctions on Iran in exchange for its verifiable move away from development of a nuclear bomb.
Obama spokesman Josh Earnest said Thursday that even the detention of three Americans in Iran and unresolved case of a fourth missing in the country would not be a barrier to a possible nuclear deal.
ABC News' Mary Bruce contributed to this report.