Can Palestinians and Israelis ever agree a deal on the sovereignty of the Holy City?
Mitchell has been pressing Israel to halt construction of West Bank settlements as a confidence-building gesture to the Palestinians.
Settlements in the West Bank, which Palestinians want for a future state, are home to 300,000 Israelis, and around 2.5million Palestinians.
Barack Obama, the US president, has said he opposes all settlement construction, while Mahmoud Abbas, the Palestinian president, has staunchly refused to reopen peace talks until Netanyahu halts all settlement activity.
A survey released on Wednesday showed freezing settlements would be an unpopular move among Jewish Israelis, with almost two-thirds of those questioned by the Maagar Mohot polling company saying they opposed the move.
Netanyahu has said he sees the emphasis on settlements as unfair, and insisted conflict in the Middle East is rooted in Arab enmity towards Israel.
The prime minister, who is travelling from London to Germany later on Wednesday, said he hoped peace negotiations between Israel and the Palestinians would resume “shortly”.
“We are making headway. My government has taken steps in both words and deeds to move forward,” he said before meeting Mitchell.
Palestinian officials have said their leader would likely meet Netanyahu on the sidelines of the UN General Assembly next month in New York.
But it remains unclear what sort of compromise would be acceptable to the Americans or the Palestinians.
On Tuesday, Netanyahu said that his government is unwilling to negotiate on the status of Jerusalem as a joint Israel-Palestinian capital.
Speaking in London at a meeting with Gordon Brown, the British prime minister, he also said that any peace talks with the Palestinians would have to cover the issue of a “demilitarised Palestine”, as well as illegal Israeli settlements in the West Bank.
Brown said that he was “increasingly confident” of progress on Middle East peace after talks with Netanyahu, whom he called “a leader of immense courage”.
Netanyahu’s talks in the UK – which also included discussions on Iran’s nuclear programme – are part of a three-day Europe tour.
On Thursday he is due to meet Angela Merkel, the German Chancellor.