US Secretary of State John Kerry and Israeli Prime Minister Benjamin Netanyahu spoke as they began talks about Israeli-Palestinian peace negotiations.
Mr Netanyahu said: "Iran must not have a nuclear weapons capability, which means they shouldn't have centrifuges and they shouldn't have a plutonium heavy-water plant, which is used only for nuclear weapons." Iran says it is enriching uranium solely for electricity and medical treatments, not nuclear weapons.
Mr Kerry took a different tack from Mr Netanyahu by suggesting Iran could show its programme was peaceful by adhering to international standards followed by other nations.
Speaking as he and Mr Netanyahu began a meeting at the US ambassador's residence in Rome, Mr Kerry said: "We will pursue a diplomatic initiative but with eyes wide open, aware it will be vital for Iran to live up to the standards of other nations that have nuclear programmes and prove those programmes are indeed peaceful."
Six global powers held talks with Iran last week to test whether a diplomatic resolution might be reached. It was their first such negotiations since the election of moderate Iranian President Hassan Rouhani in June.