Donald Trump became the first sitting U.S. president to visit the holy site, after a fraught diplomatic lead up to his trip.
Palestinians say accepting Netanyahu's call could deny Palestinian refugees of past wars any right of return.
Just the fact that Trump committed his administration to an Israeli-Palestinian peace process sends a message of defiance to the Israeli leadership.
The German minister said he would meet with the groups critical of the IDF despite the warnings.
There was no immediate reaction from the White House, which is in discussions with Israel on limiting the construction of settlements on land Palestinians seek for a state.
There is skepticism in the United States and Middle East over the chances for restarting Israeli-Palestinian diplomacy. Peace talks have been frozen since 2014.
Some commentators say a push to dissolve the government is cover to avoid a possible indictment on corruption charges.
Azaria sentence is overshadowed by news of Arab-Israeli negotiations.
Abbas said he agreed with Trump's call for Israel to refrain from settlement building in the occupied West Bank and East Jerusalem.
Trump considers Middle East peace a "high priority," the White House official said. The president has given his son-in-law, Jared Kushner, the job of negotiating a peace deal.
Israeli prime minister says he will pursue 'responsible policies' in visit to the White House.
As Trump and Netanyahu prepare for their Feb. 15 meeting, focus has shifted to Iran's ballistic missile test last week.
The legislation has been condemned by Palestinians as a blow to their hopes of statehood. But its passage may only be largely symbolic as it contravenes Israeli Supreme Court rulings on property rights.
Israeli prime minister is criticized at home and abroad for tweet praising Trump's plan to erect a wall on the Mexican border.
Police are currently investigating the Israeli leader on allegations of corruption.
The far-right Jewish Home party, along with members of Prime Minister Benjamin Netanyahu's Likud party, is promoting legislation that would effectively annex one large settlement in the occupied West Bank to Israel.
Some 570,000 Israelis now live in the Israeli-occupied West Bank and in East Jerusalem, together home to more than 2.6 million Palestinians.
Israel's mission to the United Nations said funding would be cut to U.N. bodies it described as "anti-Israel."