Obama also reiterated the US backing for international demands made of the Hamas movement - that it recognise Israel, end violence and agree to recognise previous peace agreements with Israel.
He said the US would support efforts to end weapons smuggling across the Gaza border from Egypt.
However, he called for a complete withdrawal of Israeli forces from Gaza following its offensive, and said the US would provide humanitarian and economic assistance to the millions of Palestinians living in the Gaza Strip.
Osama Hamdan, a Hamas spokesman, told Al Jazeera Obama's remarks seemed to show that the US viewed the situation through "Israeli eyes".
Mitchell, 75, acknowledged there were "many reasons to be sceptical" about the prospects for peace between Israelis and Palestinians.
"The key is the mutual commitment of the parties, and the active participation of the United States government," he said.
He is best known for helping to broker Northern Ireland's historic Good Friday agreement in 1998 which ended decades of bloody conflict.
In 2000, he also presided over a committee investigating the ongoing violence of the Middle East conflict, which recommended Palestinians do more to stop attacks on Israel and an end to Israeli settlement building on occupied land.
Obama also named Richard Holbrooke, a former UN ambassador, as his special envoy to Afghanistan and Pakistan.