Israeli officials and congressional Republicans on Monday set high bars with exacting conditions for a nuclear accord with Iran, signaling fresh domestic and international pressure on negotiations leading up to a summer deadline.

Leading Arab governments, including Saudi Arabia, cautiously accepted the landmark diplomacy with Iran, in their most detailed reactions yet. But Saudi officials said they needed more assurances that Iran’s pathway to a nuclear weapons program has been blocked.

The global responses and congressional reactions—pitted against a determined campaign by the Obama administration—form the outlines of a furious political battle as Israeli officials and their supporters gear up for a lobbying effort once Congress returns next week from an Easter recess.

“There is an alternative: to stand firm, get a much better deal, a deal that can be trusted,” Israel’s intelligence chief, Yuval Steinitz, said. “The deal has to be made on the assumption that Iran might violate it.”

President Barack Obama and his aides dismissed much of the criticism—especially Israeli demands that Iran alter its regional and foreign policy and accept Israel’s right to exist before world powers accept a deal.