"Any permanent sanctions relief demands congressional approval," they say.
The dual appearances come at a tense time in U.S.-Israeli relations.
The president reportedly urged Netanyahu to tone down his rhetoric on Iran.
Sen. Robert Menendez said White House spokesman's comments were "way over the top."
A new Reuters-Ipsos poll found 44 percent of respondents support the deal.
The secretary of State on Sunday defended the new agreement on Iran’s nuclear ambitions.
The Israeli prime minister said a proposal would have required only a “minor concession.”
Rouhani said Iran would not accept “any threat, sanction, insult or discrimination."
"There is no deal," said spokesman Josh Earnest. "Any critique of the deal is premature."
The New York Democrat is refusing to back away from his bill to impose harsh sanctions.
“We have accepted Iranian uranium enrichment,” the former NSA director said.
A restart could provide the country with weapons-grade plutonium.
In call, Obama reaffirmed “the importance of Iran following through on its commitments.”
“We’ll move forward appropriately,” the majority leader said.
"We know the sanctions got us here," the Tennessee Republican said.
“No deal is better than a bad deal,” the secretary of State said.
Kerry called the process “a very productive one,” adding that “diplomacy takes time.”