"As you know, the president has recently expressed his view that he wants to put a lot of effort into seeing if we can not advance a peace initiative between Israel and Palestine", Tillerson said.
Since the annexation, Israel has "promoted the twofold goal of expanding the city's Jewish population and reducing its Palestinian population", according to Israeli human rights group Btselem, through land appropriation, discriminatory policies in construction, unequal budget distribution, and other measures. A Fox News correspondent had claimed the opposite: that the Israeli leader asked the United States president not to move the embassy.
Trump promised to relocate the USA embassy as one of his campaign pledges but is yet to make a decision.
Israeli officials appear to be growing increasingly nervous over Trump's visit, when he is expected to make an attempt at relaunching long-stalled peace talks with the Palestinians.
The Prime Minister's Office added in its own statement at the end of the transcript, "This is the clear and consistent position of Prime Minister Netanyahu, which he reiterated today".
Trump has reportedly asked Netanyahu to slow Israeli settlement building activity in the West Bank, but the USA president has appointed a pro-settlement envoy to Israel, and the White House has failed to denounce plans for new units. Palestinians say it stems from anger over decades of Israeli rule.
However, Israel's Channel 2 reports that while planning the visit, a Trump aide questioned Israel's control over the holy site, located in disputed East Jerusalem.
Both highly sensitive issues made headlines in Israel on Tuesday as preparations intensified for Trump's visit to the country and the Palestinian territories on May 22 and 23.
The Trump administration seems to have chose to follow that path as well.
Prime Minister Benjamin Netanyahu's Office denied the claim on Monday evening, issuing a statement that said: "The things published on Fox News are a lie".
Over the weekend, the US and Israel already publicly exchanged views on the impact of relocating the US Embassy to Jerusalem on the peace process.
The spat came on the day the new U.S. ambassador to Israel, David Friedman - an orthodox Jew - arrived in the country to take up his position.
Netanyahu told Friedman his immediate visit to the Western Wall was "a strong gesture of solidarity". Earlier this month, he held a warm meeting with the Palestinian president, Mahmoud Abbas, at the White House.
But since taking office, Trump has called for restraint in settlement construction and signaled he is no hurry to move the embassy. "It will advance the process because of the correction of the historic injustice and the smashing of the Palestinian fantasy of Jerusalem not being the capital of Israel", it said.