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