Turkey is to send an inspection team to survey excavation work being carried out near the Temple Mount or Haram al-Sharif in East Jerusalem.
The Israeli prime minister is on a two-day visit to Turkey
The decision came as the Israeli and Turkish prime ministers held talks in the Turkish capital, Ankara.
The work on an ancient mound near Jerusalem's holiest site has caused widespread anger in the Muslim world.
Israel is now showing the work live on the internet in a bid to calm Muslim fears the site is being damaged.
The Temple Mount or Haram al-Sharif (Noble Sanctuary) is the holiest site in Judaism and Islam's third holiest shrine.
Israel says the work is needed to repair a walkway up to the compound and that it poses no risk to the site. But Palestinian leaders say the work threatens Islamic archaeological remains and see it as huge provocation.
Construction work has been put off while excavation continues
The start of the work last week sparked angry protests and Muslim leaders around the world have demanded it be halted. Israel has suspended building work but preparatory excavations are continuing.
Turkish Prime Minister Recep Tayyip Erdogan said the Israeli leader, Ehud Olmert, had showed him photographs of the construction, "but they have failed to convince me 100%".
"I proposed to send a technical team to inspect on site the work that is being done and he (Olmert) has agreed," he told a press conference.
Mr Olmert welcomed the move, saying Israel had nothing to hide. "We will not touch any place that is holy to both Christians and Muslims," he said.
The Israeli authorities, meanwhile, have now installed cameras to film the excavation work for live broadcast on the internet in an attempt to ease Muslim anger.
The Israeli Antiquities Authority says it wants to show that this is a proper archaeological dig.
JERUSALEM HOLY SITE
SACRED TO MUSLIMS: Site of Prophet Muhammad's first prayers and ascent into Heaven, home to al-Aqsa mosque and Dome of the Rock
SACRED TO JEWS: Site of first and second Temples and the rock on which Abraham offered his son as a sacrifice. Western Wall is the holiest site in Judaism
"There will be three cameras in the excavation area. They will show a complete angle of the excavation area," Israel Antiquities Authority official Liat Eizenkot told AFP news agency.
Daily work at the site will be broadcast from 0630 local time (0430 GMT) to 1430 (1230 GMT), the Israel Antiquities Authority said, and the web camera would remain on outside working hours.
Broadcasts have started and can be seen at the antiquities authority's website at www.antiquities.org.il/home_eng.asp.
The Haram al-Sharif is believed to be where the Prophet Muhammad made an ascent to heaven into the presence of God.
Jews believe the Temple Mount is where Abraham offered his son Isaac as a sacrifice to God. It is also the site to the First and Second Temples. The Western Wall of the mount is the holiest site in Judaism.
Israel captured East Jerusalem in the 1967 war. Since then, the compound has remained under Muslim jurisdiction in conjunction with neighbouring Jordan.