Israeli Intelligence Minister Eli Cohen, speaking on Army Radio, said a commitment towards a tough policy on Iran by the next administration in Washington would determine whether other countries would opt for normalisation deals with Israel.
Pompeo also announced a new pro-Israel policy, stating that Washington would designate as "anti-Semitic" the BDS or Boycott, Divestment and Sanctions campaign which calls for a wide-ranging embargo against Israel over its treatment of the Palestinians.
"The BDS movement for Palestinian freedom, justice and equality, stands with all those struggling for a more dignified, just and lovely world", it said.
Last year, Trump's administration made the controversial decision to recognise Israeli sovereignty in the Golan - a move Pompeo on Thursday called "historically important and simply a recognition of the reality".
During his trip, Pompeo is expected a visit Psagot, an illegal Israeli settlement near Ramallah and the site of a winery that has produced a label carrying his name.
Tom Cotton of Arkansas, Marco Rubio of Florida, Ted Cruz of Texas and Kelly Loeffler of Georgia wrote a letter to US President Donald Trump.
Pompeo did not provide additional details about the initiative, and it was unclear what organizations would be at risk of losing funding.
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A small but growing number of Republicans are also backing calls for the president-elect to be given daily intelligence briefings. All of Trump's tweets were flagged as being disputed and potentially misleading.
Pompeo warned the Islamic republic in comments Wednesday that the deals the UAE and Bahrain have reached with Israel showed "its influence in the region is waning". Amnesty does not take a position on the boycott movement.
"It's quite ironic, really, that such a xenophobic, racist USA administration that is a partner in Israeli crimes against the Palestinian people, and that is empowering white supremacists and anti-Semites ... would dare to smear a human rights movement led by Palestinians calling for justice for the entire Palestinian people", said BDS co-founder Omar Barghouti during an interview with Al Jazeera. The U.S. House of Representatives passed a resolution opposing the boycott movement previous year, and several U.S. states have enacted anti-BDS laws.
Pompeo made the comments during a joint appearance with Israeli Prime Minister Benjamin Netanyahu, who interrupted the USA diplomat's speech to tell him the announcement "sounds simply wonderful". In 2019, Pompeo broke with decades of American foreign policy to announce that the USA under Trump no longer viewed Israel's settlements as "inconsistent with worldwide law".
Israel captured the West Bank from Jordan during the 1967 war.
The Palestinians want both territories to be part of their future state and view the settlements as a violation of global law and an obstacle to peace - a position endorsed by most of the worldwide community.
"With our many partners, we shall resist these McCarthyite attempts to intimidate and bully Palestinian, Israeli and global human rights defenders into accepting Israeli apartheid and settler-colonialism as fate", the BDS statement concluded.
Neither Netanyahu nor Pompeo said anything about the US election.
Pompeo - who has so far backed Trump in refusing to concede defeat to President-elect Joe Biden - is on what could be his final Europe and Middle East tour in the post.