US President Barack Obama, delivering a keynote speech to Israeli students, said on Thursday that continued settlement activity was “counterproductive” to peace and urged Israelis to accept the Palestinians’ right to self-determination.

But he also insisted that now was the time for the Arab world to “take steps toward normalising relations” with the Jewish state, which has been shunned by most of its neighbours.

“Israelis must recognize that continued settlement activity is counterproductive to the cause of peace, and that an independent Palestine must be viable, that real borders will have to be drawn,” Obama said in a nationally televised speech to an Israeli public that has given him a rousing welcome despite lingering suspicions about his diplomatic policies.

Obama, coupling his push for a more conciliatory Israeli approach to the Palestinians with a reaffirmation of his commitment to Israel’s security, also promised that Washington will “do what we must to prevent a nuclear-armed Iran”.

Speaking after a visit to the occupied West Bank for talks with Palestinian leaders, Obama also insisted that “Palestinians must recognize that Israel will be a Jewish state, and that Israelis have the right to insist upon their security”.

But he warned Israelis: “Given the demographics west of the Jordan River, the only way for Israel to endure and thrive as a Jewish and democratic state is through the realisation of an independent and viable Palestine.”“Given the frustration in the international community, Israel must reverse an undertow of isolation,” Obama said.

Some in the crowd heckled Obama at one point, but the president – who has made outreach to ordinary Israelis a main thrust of his visit – received rounds of loud applause for his comments on the need for peace with the Palestinians.

US-sponsored talks between Israel and the Palestinians broke down in 2010 over the issue of Jewish settlements and Palestinian President Mahmoud Abbas repeated on Thursday that he wanted to see construction halted on land seized by Israel in the 1967 Middle East war.

Obama, who met Israeli Prime Minister Benjamin Netanyahu on Wednesday, agreed in Ramallah that settlement building did not “advance the cause of peace”, but stopped short of demanding a construction freeze to enable stalled negotiations to resume.

Back in Jerusalem addressing Israelis, he did not shy away from the volatile settlement issue or criticism of the impact of Israeli occupation.

“It is not just when settler violence against Palestinians goes unpunished. It is not right to prevent Palestinians from farming their lands; to restrict a student’s ability to move around the West Bank; or to displace Palestinian families from their home,” he said.

“Neither occupation nor expulsion is the answer”.But Obama also sought to convince Israelis he understood the deep and ancient Jewish ties to Israel, seeking to correct an impression that he was less than appreciative of their history.