Upon his arrival at the airport, Mitchell briefly met Javier Solana, the EU foreign policy chief, who is in Egypt to discuss shoring-up Hamas' and Israel's ceasefires in Gaza.
Solana said the EU was "supporting wholeheartedly the efforts of Egyptians to find a reconciliation among the Palestinians that can leade to a government".
Asked in an interview with Al Jazeera if this meant that the EU would accept a Palesinian unity government that included Hamas, Solana said: "We want for the Palestinians to have a dialogue [with the EU] but of course we need a government that is compatibile with the ideas that the Europeans defend - which is a two-state solution and we support also the Arab Peace Initiative."
Obama has vowed to make the Israeli-Palestinian conflict a priority and described Mitchell as the man who "speaks for us" on Middle East issues.
George Bush, Obama's predecessor, had been widely criticised for neglecting the Middle East for much of his tenure.
"The charge that Senator Mitchell has is to engage vigorously and consistently in order for us to achieve genuine progress," Obama said.
"And when I say progress, not just photo ops, but progress that is concrete."
Mitchell's Middle East tour was launched as Obama gave his first television interview to an Arab broadcaster, pledging his administration would take a wider view of the region.
Speaking to Al Arabiya, Obama said the US remains committed to protecting its long-time ally Israel, but said he also believes there are Israelis who recognise the need for regional peace and are willing to make the necessary sacrifices to achieve it.
"I think the most important thing is for the United States to get engaged right away," he said.
Commenting on Mitchell's visit to the Middle East he said: "What I told him is to start by listening ... because all too often the United States starts by dictating."
In 2000, Mitchell led a fact-finding committee on Middle East violence that recommended commitments by Israel and the Palestinian Authority to immediately and unconditionally end their fighting.
"Conflicts are created, conducted and sustained by human beings. They can be ended by human beings"
US envoy for Middle East peace
His report, released in April 2001, urged Israel to freeze settlements in the West Bank and the Palestinians to cease rocket attacks across the border, the two issues that remain sticking points today.
Robert Wood, a spokesman for the US state department, said Mitchell might travel to the Gaza Strip, where Israel waged a 22-day war on the territory that left more than 1,300 Palestinians deadbefore declaring a ceasefire on January 18.
Thirteen Israelis, three of them civilians, were also killed in the conflict.
Wood said Mitchell will work to consolidate the Gaza ceasefire, help in preventing alleged arms smuggling by Hamas and facilitate the opening of border crossings.
Mitchell's report will also help formulate the new administration's overall policy toward the Middle East, Wood said.
Ziad Hafez, managing editor of the journal Contemporary Arab Affairs, told Al Jazeera that he doubts about whether Mitchell will achieve much in his new role.
"I don't think any movement is going to take place as long as the fundamental rules are not observed - which means that if you don't talk to the principal parties, nothing much will be accomplished," he said.
"Neither the Palestinian Authority nor the Egyptian government can provide any leverage over the situation in [Hamas-run] Gaza.
"Mitchell already had a previous mission in the Middle East and it did not amount to much, so I don't know what he will do now. As long as there is no political will in the United States to work seriously in promoting the Arab peace initiative [on Israeli-Palestinian relations], I don't think a lot will be accomplished."
Mitchell, 77, is credited with persuading all sides in the Northern Ireland conflict to sign up to a power-sharing deal, culminating in the landmark Good Friday peace accord in 1998.