"The president is being very careful to understand how such a decision would impact the peace process", Tillerson said.
"It would advance it by fixing a historic wrong and shatter the Palestinian illusion that Jerusalem is not the capital of Israel".
US Embassy in Tel Aviv.
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 report on Fox News is a lie" and "Netanyahu supports moving the U.S. Embassy to Jerusalem", his office said in a statement.
A senior Israeli official said that Netanyahu expressed his desire that the embassy be moved to Jerusalem in his meetings with Trump and Tillerson during his latest visit in Washington.
Trump had promised during the presidential campaign to move the USA embassy from Tel Aviv to Jerusalem, which would upend US policy in the Middle East.
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During his presidential campaign, Trump controversially promised to move the embassy and to recognize Jerusalem as Israel's "undivided" capital. He has told Trump that Palestinians are intractable negotiating partners who make demands that Israel can not meet.
Trump's administration has been sending mixed messages in its dealings with a right-wing Israeli government that had hoped for a more sympathetic attitude from the Republican president after a rocky relationship with his Democratic predecessor, Barack Obama.
The new US Ambassador, David Friedman, just arrived in Israel and his first visit was to the Western Wall where he said he "prayed for the president".
Now no country has an embassy in Jerusalem, while 86 nations maintain consulates in Tel Aviv.
"This is Prime Minister Netanyahu's consistent and clear stance", his office clarified.
The unusual release came after a Fox News reported that Netanyahu asked Trump not to move the us embassy to Jerusalem at this point.
"We wanted to come straight to the holiest place in the entire Jewish world, the "Kotel HaMaaravi", the Western Wall, straight from the airport", Friedman told reporters. He is scheduled to meet Netanyahu in Jerusalem before travelling to Bethlehem to meet with Palestinian President Mahmoud Abbas. Israel continues to expand illegal settlements on the territory that would be a part of a future Palestinian state.
Trump's rise has now emboldened Israeli extremists to implement their illegal policies and further their occupational agenda by transferring the embassy, a move that Palestinian officials and prominent American politicians have cautioned against.