The half-built structure was erected by Israel in the midst of the Gaza conflict in early August, triggering outrage from Jordan which overseas Muslim heritage sites in Jerusalem.
It ran alongside a bigger wooden structure -- the Mughrabi ramp -- that leads from the Western Wall plaza up to the Al-Aqsa mosque compound in Jerusalem's Old City.
The Mughrabi ramp is the only access to the plaza for non-Muslims.
Anything that is viewed as changing the status quo in or around the flashpoint Al-Aqsa compound, which houses the third-holiest site in Islam, is highly sensitive and triggers a strong response from Jordan.
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That move was hailed by Jordan and by this afternoon most of the new ramp had been taken down, an AFP correspondent said.
The ramp's construction is a politically charged issue because each side claims authority over it.
Israel argues that because the ramp is located outside the Al-Aqsa compound, it should oversee the construction.
And Jordan insists that since the ramp leads to the mosque compound, it should manage or at least be consulted over any new construction plans.
Jordan's Waqf is the religious body that oversees the compound and other Islamic sites in Jerusalem.
"We think it was the start of a new, permanent ramp," he told AFP.
The existing Mughrabi ramp, which is also wooden on a metal framework, was built in 2004 after its predecessor collapsed.