The former president said two states were the only viable solution for the Israeli-Palestinian conflict and that he would be reporting his findings from his trip to Gaza and the Middle East back to Barack Obama, the US president.
He said he supported the proposition made by Obama in his speech in Cairo earlier this month, with regard to how to achieve peace in the Middle East.
Carter said: He [Obama] mentioned several things about the prospective road to peace.
"First of all, all settlement expansion should be stopped immediately.
"Secondly, that Jerusalem should be shared. Third, that there should be a two-state solution ... each occupying their own territory.
"Fourth that these two nations should live in peace."
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said: "The symbolism [of the visit] is important, raising the issue of the suffering of the Palestinian people through the international media following Carter through Gaza."
Carter is believed to have delivered a note to Haniyeh from the parents of captured Israeli soldier Gilad Schalit, who has been held since 2006.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said: "The Israelis will take from Carter what he can offer, for example, the fact that he was able to carry a letter from the family of Gilad Schalit, a letter which will be presumably delivered to Schalit.
"But his criticism won't be taken that seriously given that he is not speaking on behalf of the US administration."
Mohyeldin said that Carter had earlier met with families of Palestinian prisoners, including an eight-year-old girl who had never met her father as he has been in an Israeli jail since she was born.
"So he [Carter] is taking back with him a letter from the Palestinian people to give to Israeli officials, so certainly in that capacity he is also acting as a semi-official mediator between Palestinians and Israelis," Mohyeldin said.
Israel launched its 22-day offensive against Gaza's Hamas rulers and the Gazan people on 27 December.
|Israel's offensive in Gaza destroyed thousands of Palestinian homes [AFP]
The operation killed more than 1,400 Palestinians, including more than 900 civilians, among them scores of children, according to Palestinian officials and human rights groups.
It also destroyed thousands of homes and heavily damaged Gaza's infrastructure.
Israel claims the death toll was lower and most of the dead were Hamas fighters.
Thirteen Israelis were also killed during the fighting.
Rebuilding Gaza is being hampered by Israel's blockade of Gaza which dates back to June 2007 when Hamas took control of the territory.
Since then, Israel and Egypt, which control Gaza's only border crossing that bypasses Israel, have kept the territory of 1.5 million aid-dependent people sealed to all but essential humanitarian supplies.
Israel has insisted that the blockade is necessary to prevent Hamas from arming itself, but human rights groups say it is a collective punishment.
Carter met with Hamas' exiled leadership in Syria on Thursday and said they wanted "peace and they want to have reconciliation, not only with Fatah brothers but also eventually with the Israelis".