Recep Tayyip Erdogan said Olmert had shown him photographs of the construction work, but had failed to convince him that it would not harm the holy sites there.
The Israeli premier agreed to a Turkish suggestion for a technical team from Turkey to inspect the site, Erdogan said.
"Israel should respect the holy places rather than increase tensions," Erdogan said Thursday ahead of his meeting with Olmert.
Erdogan said that "any action taken at the Temple Mount will stir a reaction and turmoil in the Arab world. Israel should respect all the international agreements meant for protecting the places holy to Islam in Jerusalem."
Peace with Syria
In a joint press conference following the meeting with Erdogan, Olmert said that Israel wanted to make peace with Syria, but he urged Damascus to stop supporting terrorism.
"We want to make peace with Syria, if there is a peace we will be satisfied and be happy," Olmert said. "We especially want Syria to stop supporting terrorism and abide by the rules set up by the international community."
On the Palestinian front the Israeli prime minister said the new Palestinian government must "openly and
clearly" agree with the demands of the Quartet of the Middle East negotiators, including the recognition of the Jewish State.
The Quartet - the US, EU, Russia and UN - have demanded that Hamas renounce violence, recognize Israel's right to exist and accept past peace agreements.
Ronny Sofer contributed to the report