Mitchell is also expected to discuss progress on peace negotiations with Tzipi Livni, leader of the opposition Kadima party.
Shortly after arriving in the country on Wednesday evening, Mitchell met Ehud Barak, Israel's defence minister.
Netanyahu said on Sunday that his government will resume peace talks with Mahmoud Abbas, the Palestinian president, but has not committed to the idea of a two-state solution.
The new Israeli administration has also not ordered a halt to the building of illegal Jewish settlements on occupied Palestinian land.
The US and the European Union have repeatedly called on Netanyahu to hold fresh talks with Abbas and signal that his government is sincere about establishing a Palestinian state alongside Israel.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said: "This is something that [US President Barack] Obama has overtly, clearly and unambiguously committed himself to in speeches that he made to Europe in the last few weeks.
"He really did state the US commitment to the two-state solution as being the shape for a final agreement between the Palestinians and the Israelis."
However, Netanyahu has said that he wants any talks with Abbas to focus mainly on security and economic issues.
Furthermore, Lieberman, an Israeli nationalist, has flatly rejected a restart of the Israeli-Palestinian talks launched in 2007 by George Bush, the former US president.
Mitchell is set to meet Abbas and other Palestinian leaders in the Israeli-occupied West Bank on Friday.
Mitchell's talks on Thursday coincided with a march by nationalist Jews towards the compound of al-Aqsa mosque in Jerusalem.
Hundreds of people headed to the site to hold a prayer vigil there, angering Palestinians living in the city.
The Palestinian cabinet responded by calling on Palestinians to head to the mosque to defend it.
None of the Jews who marched to al-Aqsa mosque actually entered the compound, our correspondent reported.
"There was a threat - and it was taken seriously - because the whole of the old city of Jerusalem has been cordoned off by police," she said.
"But we have not seen any attempt by Jews to enter the al-Aqsa compound. If you like, there has been a bogus threat, purely designed to provoke the Palestinian side and cause them inconvenience."
The Israeli authorities banned all Palestinian men under the age of 50 from entering al-Aqsa mosque.
"It is a very interesting example of how a threat by a Jewish group, many of them living in illegal settlements, can make the Israeli police jump into action and cause very strong feelings on the part of the Palestinians living in Jerusalem."