Trump's speech drew on the symbolic nature of his first foreign trip, as he has jetted from Saudi Arabia, the birthplace of Islam, to Israel and then to the Vatican on Tuesday night, calling on members of the three faiths to "set aside our sectarian differences" and work toward peace.
Trump reportedly told Lavrov and Russian Ambassador Sergei Kislyak at a meeting this month about an Islamic State threat using laptops on planes, including highly classified details about the origin of the intelligence, which came from a "partner" later reported to be Israel.
Trump visited the Western Wall without any Israeli government officials by his side despite requests from Israeli officials.
US President Donald Trump has wrapped up a two-day visit to Israel and the Occupied Territories where he met Benjamin Netanyahu, the Israeli prime minister, and Palestinian Authority President Mahmoud Abbas.
Trump had promised during his campaign that he would recognize Jerusalem as Israel's capital, which now the US and most of the worldwide community does not, and move the USA embassy from Tel Aviv to Jerusalem.
The United States welcomed the move but the Palestinians said they had heard such promises before.
Turkey blocks visit to German soldiers at air base
The move came after Germany granted asylum to soldiers whom Turkey believes were involved in last year's failed coup attempt. Germany and other Western allies have voiced concern about what they fear is a drift towards authoritarian rule in Turkey.
"If not, you'll be blamed because I just put it on record", Trump quipped.
During his talk at the Israel Museum, Trump placed the blame for the lack of a reached settlement between Israelis and Palestinians at the door of the Palestinians.
Trump, responding to a journalist's question on the subject alongside Netanyahu, said "I never mentioned the word or the name Israel".
Trump was introduced by Netanyahu, who thanked the USA leader for his "steadfast" support of the Jewish people. He also expressed his wishes for Trump to be the United States president who succeeds in brokering peace between Palestinians and Israelis.
"Conflict can not continue forever", he said.
Dershowitz praised Trump for declaring during the visit to Israel that Iran must "never" be permitted to develop nuclear weapons, contrasting it to an agreement with the Iranians made by former President Barack Obama.
Trump on Tuesday also visited the Holocaust memorial Yad Vashem, where he and first lady Melania Trump laid a wreath in honor of concentration camp victims.