The U.S., one of Iran's toughest critics, has welcomed Iran's more moderate tone under Rouhani and has urged Iranian officials to seize the moment in reducing nuclear tensions.
On Monday, Iran's nuclear chief, Ali Akbar Salehi, said the chances for a breakthrough have improved thanks to unity among the new Iranian leadership over what it will seek in the next round of negotiations. He did not elaborate. But Iran wants an end to the economic and political sanctions it faces over fears it is progressing to nuclear weapons ability.
Netanyahu, however, urged the world to stand tough and make four key demands, most importantly that Iran stop enriching uranium a potential pathway to producing a nuclear weapon.
According to the Israeli leader, the other three demands should be that Iran remove its existing stockpile of enriched uranium, close its enrichment facility in the central city of Qom and stop producing plutonium, which can also be used for nuclear arms.
"Until all four of these measures are achieved, the pressure on Iran must be increased and not relaxed, and certainly not eased," Netanyahu said. He reiterated his belief that all diplomatic efforts must be accompanied by a "credible military threat."
Netanyahu has said the threat of military action was key to ensuring the success of the new U.S.-Russia plan to destroy Syria's chemical weapons program. Syria is a close Iranian ally.
In his address to the U.N. General Assembly last year, Netanyahu presented a cartoon-like drawing outlining what he said was Iran's march toward nuclear weapons.
At the time, he said that Iran would reach the "final stage" of enrichment by mid-2013 at the latest.
Israeli officials say the timeline presented was based on available information at the time and that Netanyahu's "red lines" remain the same.
Israel has repeatedly hinted it is prepared to take military action against Iran if international diplomacy fails to halt the nuclear program.