Earlier on Monday, U.S. Secretary of State Condoleezza Rice warned Tehran it faced more sanctions if it flouted the two-week deadline.
Before Brown spoke, the speaker of the parliament, Dalia Itzik, said it was unbelievable that 63 years after the Holocaust, "we are again facing the threat of extermination from the Iranians, with whom we have no conflict".
PEACE
Brown, who began his speech with the Hebrew phrase for "peace be with you", said a historic peace with the Palestinians was within Israel's grasp. He urged Israel to freeze the expansion of Jewish settlements in the occupied West Bank and to withdraw from them in a future peace deal.
That comment drew heckling from one person in the chamber but Brown received a standing ovation at the end of his speech.
Brown described the current leadership of the Palestinian Authority as the best partner Israel has had for peace in a generation and said it must fulfil its security obligations.
Speaking to reporters on Sunday evening, Brown said Iran had broken the terms of the nuclear Non-Proliferation Treaty and had "misled the international community about the scale of their preparations for weaponry".
The United States has refused to rule out military action against Iran if diplomacy fails to resolve the nuclear row.
Israel, long assumed to have nuclear arms, has sworn to prevent Iran from obtaining atomic weapons. An Israeli air force drill last month raised speculation it was planning an attack.
A senior Iranian official was quoted this month as saying Iran would destroy Israel and 32 U.S. military bases in the Middle East if the Islamic Republic was attacked.
