Ahmed Yousef, a senior adviser to Mr. Haniyeh, also acknowledges Carter's ties with Obama and potential to act as a go-between with the US, which considers Hamas to be a terrorist group. As a result, Obama's Middle East envoy, George Mitchell, has not met with Hamas leaders.
"He is close to President Obama and nobody in his type of position understands the conflict with all its problems like he does," says Mr. Yousef in a phone interview. "I think he will give Obama the information and analysis he needs to address this conflict in a proper way and to restore the image of America in the region after two decades of failed diplomacy."
Hamas reportedly thwarted two bombs targeting Carter's vehicle on Tuesday, according to Israeli newspaper Haaretz and news agencies.
Carter to Hamas: Accept US conditions for talks
On Tuesday in Gaza and last week in the Syrian capital, where Hamas chief Khaled Meshaal lives, Mr. Carter urged the militant group ruling Gaza to accept the conditions for talks laid out by the international community, including renouncing violence, accepting previous Israeli-Palestinian agreements, and recognizing the Jewish state's right to exist.
"I called on Hamas leaders that I met with in Damascus and I told Hamas leaders in Gaza today to accept these conditions," said Carter to reporters after meeting with Haniyeh for the first time. "They made several statements, and showed readiness to join the peace [process] and move towards establishing a just and independent Palestinian state."