Trump was referring to US media reports according to which he disclosed to Lavrov and other Russian officials intelligence that Israel had passed on to America about plans by the Islamic State to blow up airplanes using laptop computers.
Trump reportedly shared sensitive intelligence with the Russians about ISIS, with speculation that the information shared came from Israeli intelligence sources.
"Never mentioned it during our conversation", Trump said to reporters before his private meeting with Israeli Prime Minister Benjamin Netanyahu.
Israel has also expressed concern about the $110bn (£84.6bn) arms deal announced between the USA and Saudi Arabia on Saturday, with a senior cabinet minister describing the kingdom as a "hostile country".
En route to Tel Aviv from Riyadh, Saudi Arabia, aboard Air Force One, Tillerson balked at the idea of the president saying sorry for sharing that information without first telling Israel.
US President Donald Trump said on Monday that Iran must immediately stop its financial and military support for "terrorists and militas" and he reiterated that it never be permitted to possess atomic arms. Trump, who had promised during the campaign to move the U.S. Embassy from Tel Aviv to Jerusalem but has since backed away from the pledge, told Bennett, "That's a good one", according to the AP.
The president, donning a yarmulke, solemnly placed his hand on the Western Wall and, after taking a few moments, left a note behind.
Trump's vision of the possibility to settle the conflict between Palestine and Israel is rather clear, and his hopes for peace already appear buoyed by his first visit to the Middle East.
Trump's schedule Monday includes meetings with both leaders, as well as a visit to the Western Wall, an important Jewish holy site.
President Donald Trump with Israeli Prime Minister Benjamin Netanyahu at an official welcoming ceremony on the president's arrival at Ben Gurion International Airport in Tel Aviv, May 22, 2017. "But we can only get there working together", he added.
"In the Middle East, an area that suffers from terrorism and madness, the alliance between the United States and Israel shines like a beacon of liberty and progress", Rivlin said.