Carter, a chief defender of the U.S.-designated terror group, said Tuesday he will meet with officials in the Obama administration in two days to discuss his latest trip to the Middle East.
Meanwhile, two Palestinian sources told FOX News that the group had discovered two roadside bombs planted near a crossing between Israel and Gaza on a path Carter's convoy took to meet with the group's leaders -- Hamas advisers, though, reportedly cast doubt on claims that extremists were trying to kill Carter.
Carter was granted special waivers by the U.S. Secret Service allowing him to enter Gaza. Employees of the U.S. executive branch are not allowed into the strip since a roadside bomb killed three U.S. security personnel in 2003.
Carter was visiting with Hamas leaders to try to persuade them to accept the international community's conditions for ending its boycott of the Islamic militant group.
The international community has asked Hamas to recognize Israel, renounce violence and accept previous peace deals as part of ongoing efforts for Palestinians overall to acquire their own country. Hamas has refused.
Carter said he feels personally responsible that American weapons were used to fight in Gaza Strip last year, when Israeli Defense Forces entered the strip to stop the launch of rockets from there into Israel.
Hamas is considered a terrorist group by the U.S. and Europe and has been shunned by much of the world. Israel and Egypt have kept Gaza's borders virtually closed since Hamas overran the territory in 2007, two years after Israel withdrew from Gaza in a handover to Palestinians.
According to two eyewitnesses, including a 15-year-old boy, the bombs that were found were intended to hit Carter's vehicle as he exited Gaza. There is some suspicion that Hamas extremists linked to Al Qaeda may be behind the attempt.
The boy told FOX News he saw three Palestinian men planting bombs, four of which were later found near a mound less than a mile from the Israel-Gaza border. The boy said he notified Hamas police, who detonated the bombs and took the three men into custody.
But two Hamas advisers, in interviews with WorldNetDaily, denied reports that extremists were potentially behind such an alleged assassination attempt.
"Nobody in Gaza will touch this man," Hamas adviser Ahmed Yousef said. "He is on a noble mission. Everyone here respects him."
FOX News' Reena Ninan and The Associated Press contributed to this report.