The Israeli Prime Minister's office said it was shocked by the comments and said it had asked the United States to explain what was meant by them.
According to Israel's Channel 2 News, a member of the US delegation preparing for Trump's visit made the comment about the wall when Israeli officials suggested a photographer shoot video of the President during a proposed visit to the site.
The Israeli officials were reportedly told that the President's visit to the site was private and that he did not want Prime Minister Benjamin Netanyahu to accompany him there; the American official reportedly added that Israel did not have jurisdiction over the area.
"Israel is convinced that this statement is contrary to the position of President [Donald] Trump, as expressed in his firm opposition to the most recent UN Security Council Resolution," the Israeli Prime Minister's Office said in a written statement Monday.
A White House spokesman later told CNN: "These comments were not authorized by the White House. They do not reflect the US position, and certainly not the President's position."
The US embassy in Israel told CNN it had no comment to make.
Israel assumed control over all of Jerusalem in 1967 following the Six-Day War. Palestinians and most of the international community regard all or part of East Jerusalem as the capital of a future Palestinian state. Israel began its occupation of the West Bank at the same time; the occupation is regarded as illegal by most countries, though Israel disputes that.
The spat came on the day the new US ambassador to Israel
, David Friedman -- an orthodox Jew -- arrived in the country to take up his position.
Immediately after landing in Tel Aviv, Friedman traveled to Jerusalem and visited the Western Wall, praying for the health of his family and for the success of President Trump.
Friedman, who has long argued for recognizing Jerusalem as Israel's capital, and previously called the two-state solution a "scam," presented his credentials to Israeli President Reuven Rivlin on Tuesday.
In prepared remarks, Friedman said the Ambassadorship was the greatest honor of his life and promised to "support the state of Israel in every way and in all ways." He made no reference to suggestions the US embassy might be moved from Tel Aviv to Jerusalem
Trump has two weeks to make that decision, before the embassy automatically moves based on a 1995 US law mandating the location switch. Every President since then -- Republican and Democrat -- has waived the embassy move every six months, citing national security concerns.