"Unfortunately the Middle East finds itself in the shadow of a nuclear threat," he told delegates.
"Historically Iran sought to enrich mankind. Today, alas, Iran's rulers want to enrich uranium," he said, referring to claims it aims to produce a nuclear weapon.
Tehran denies the claims and insists its nuclear programme is solely for peaceful energy purposes.
Aipac is supporting US legislation, unveiled last week, that would give Obama powers to place sanctions on firms that export gasoline to Iran.
Peres is the first senior Israeli official to visit Obama since he took office in January and since Benyamin Netanyahu, the right-wing Israeli prime minister, came to power in March.
He said Israel's position towards peace negotiations with the Palestinians remained the same as Washington's.
"Today, there is no difference between the American position and our position," Peres said.
"We want to move ahead as swiftly together as it is needed and as it is possible."
Peres's speech was interrupted briefly by protesters criticising Israeli policies in the Gaza Strip.