He also railed against Iranian President Mahmoud Ahmadinejad's "abhorrent" threats against Israel and declared that Britain stands alongside the Jewish state.
Brown, who held talks with Israeli and Palestinian leaders on Sunday, said peace was within their grasp, but only if Israel withdraws from settlements in the occupied West Bank and the Palestinians stamp out "terrorists".
His comments on Iran's nuclear drive echoed a warning by US Secretary of State Condoleezza Rice that Tehran had two weeks to respond seriously to an international offer or face further "punitive measures."
"Iran now has a clear choice to make: suspend its nuclear programme and accept our offer of negotiations or face growing isolation and the collective response not of just one nation but of all nations round the world," Brown said.
"Just as we have led the work on three mandatory sanctions resolutions of the UN, the UK will continue to lead — with the United States and our European Union partners — in our determination to prevent an Iranian nuclear weapons programme."
The White House, meanwhile, signalled that it expected Iran to reject the US-backed incentives package.
"It is the position of the P5-plus-one that Iran should suspend its uranium enrichment, that we provided a very generous incentives package that they apparently are going to miss an opportunity to accept," said a spokeswoman.
In Paris, Solana also said a negative response from Iran would likely trigger further sanctions.
"Our relationship with Iran is a relationship of tracks, the political track, the diplomatic … but at the same time a commitment to continue in New York," he told reporters after a meeting with European MPs.
"If there is no agreement on this, the United Nations will continue."
Prime Minister Ehud Olmert said that Israel "highly appreciates" Brown's "determination… (on the) issue of terrorism and Iranian nuclear armament.
"The most serious threat for stability in the Middle East and the global peace is rooted in… Tehran," he added.
Brown was introduced by parliament speaker Dalia Itzhik, who said "the Iranian nuclear spearhead is directed not only towards Israel but towards the entire West."
Brown's spokesman said the premier did not rule out "extended sanctions in some form on the oil and gas sector" in Iran, OPEC's number two producer.
"Our focus at the moment is on strengthening the sanctions regime to keep up the pressure on Iran," he said.
Sources said that could involve sanctions on spare parts for Tehran's fairly limited domestic oil refining capacity.
In his speech, Brown also took on Ahmadinejad, who has repeatedly attacked Israel's right to exist and said its arch-foe should be wiped off the map.
"To those who question Israel's very right to exist, and threaten the lives of your citizens through terror, we say: the people of Israel have a right to live here, to live freely and to live in security," he said.
"And to those who believe that threatening statements fall upon indifferent ears, we say in one voice: it is totally abhorrent for the president of Iran to call for Israel to be wiped from the map of the world."
Brown, on his first visit to Israel and the West Bank since becoming prime minister in June 2007, held talks with leaders on both sides on Sunday in a bid to help advance the faltering peace process.
US-led negotiations were revived in November but have made little visible progress since, with Israel's continued settlement expansion in the West Bank a key bone of contention.
Brown, whose predecessor Tony Blair is now the Middle East Quartet's envoy, has pledged new aid for the Palestinians to help kick-start their struggling economy while calling for Israel to halt settlement activity.
"I believe that a historic, hard-won and lasting peace that can bring security on the ground is within your grasp… I urge you to take it by the hand," Brown told the Knesset.
However, it depended on the Palestinians stamping out "terrorists" and "Israel freezing, and withdrawing from, settlements".
