Carter said reconciliation between Hamas and Fatah, the faction led by Mahmoud Abbas, the Palestinian president, had been "objected to and obstructed by the US and Israel".
He hoped the new Obama administration would work to bring the Palestinian factions together.
The US government has branded Hamas as a terrorist group and Barack Obama, the new US president, has reiterated international demands that it recognise Israel, renounce violence and recognise previous peace agreements before it can sit at the negotiating table.
Abbas sacked a unity government led by Hamas in 2007, leading to Hamas's takeover of the Gaza Strip, while Abbas' Palestinian Authority remained in charge of the West Bank.
Carter also said Hamas had mainly kept to its truce agreement not to attack Israel.
The truce ended last December and was followed by a massive 22-day Israeli assault on Gaza that left more than 1,300 Palestinians dead.
Israel says the operation was necessary to stop Palestinian fighters firing rockets into southern Israel.
Carter said that US presidents had officially backed UN resolutions calling on Israel to end its occupation of Palestinian land, but that they had been unwilling to take on Israel's political allies.
"The fact is that very few of the presidents have been willing to confront Israel's forces in the United States, politically speaking," Carter said in what appeared to be a reference to the powerful Israeli lobby.
Carter, a Democrat who was president from 1976 until 1980, praised Obama for signalling deeper US involvement in the quest for Middle East peace by appointing Mitchell.
"If you look at US Middle East envoys in the past, almost all of them have been closely associated with Israel, sometimes even working professionally for Israel. George Mitchell is a balanced and honest broker compared to the others."
Mitchell, a former senator, has held talks in Israel and Egypt during his first tour of the region aimed at promoting what he said would be a bid for "lasting peace" between Israel and the Palestinians.
He had served as special envoy to Northern Ireland during the Clinton administration and brokered the landmark Good Friday accord in 1998 that ended decades of bloody violence in the conflict.