Mr. Carter also laid a wreath at the grave of Yasser Arafat, whom the Bush administration and many Israelis blame for the breakdown of peace talks seven years ago and the violence that followed.
At a reception in the West Bank town of Ramallah organized by Carter's office, the former president hugged Nasser Shaer, a senior Hamas politician, meeting participants said. Embraces between men are a common custom in Arab culture.
"He gave me a hug. We hugged each other, and it was a warm reception," Shaer told The Associated Press. "Carter asked what he can do to achieve peace between the Palestinians and Israel ... and I told him the possibility for peace is high."
Mr. Carter's office refused to comment, saying he does not discuss closed meetings.
Shaer, who served as deputy prime minister and education minister in the Hamas-led Palestinian government that unraveled last year, is considered a leading member of the Islamic militant group's pragmatic wing. After a stint in an Israeli prison last year, he is now a professor at a West Bank university, teaching comparative religion.
Israeli Foreign Ministry spokesman Yigal Palmor said Carter's meeting with Hamas "dignified" a group committed to Israel's destruction. "One cannot but wonder how this attitude is supposed to promote peace and understanding," he said.
Israel and the West Bank are the first stops on a visit that also is to include Saudi Arabia, Egypt, Jordan and Syria - where the virulently anti-Israel Hamas movement is headquartered. Shunned by his Israeli hosts and criticized by the White House for his willingness to meet with Hamas, Mr. Carter has urged that both stop isolating the militant group.
"Since Syria and Hamas will have to be involved in a final peace agreement, they have to be involved in discussions that lead to final peace," Mr. Carter said Tuesday.
The U.S. has also expressed displeasure at Mr. Carter's overtures to Hamas, an Islamic group responsible for the deaths of some 250 Israelis in suicide bombings and labeled a terrorist organization by both countries. Mr. Carter is to meet Khaled Mashaal, the group's exiled leader, in Damascus, Syria, on Friday.
State Department officials have treated the situation one strictly by the book, reports CBS News State Department reporter Charles Wolfson. President Carter is now a private citizen and is, therefore, entitled to meet with anyone he chooses. As a courtesy to the former president, Assistant Secretary of State for Near East Affairs David Welch did brief Mr. Carter by telephone and, according to department spokesmen, reiterated administration policy that advised against meeting anyone from Hamas, reports Wolfson. That piece of advice was clearly ignored by Mr. Carter, to no one's surprise at the State Department.
"We gave him our advice and he responded in his usual fashion which is to follow his own counsel," said one official.
Last Friday, U.S. Secretary of State Condoleezza Ricefor his plans to meet Mashaal.
"I find it hard to understand what is going to be gained by having discussions with Hamas about peace when Hamas is, in fact, the impediment to peace," Rice said at a press event with German Foreign Minister Frank-Walter Steinmeier.
Israeli Prime Minister Ehud Olmert is not meeting with Mr. Carter during his visit, and the only Israeli leader to host him, President Shimon Peres, scolded Mr. Carter for his planned meeting with Mashaal.
Critics say also say engaging Hamas will undermine moderate Palestinian President Mahmoud Abbas as he tries to make peace with the Jewish state. Abbas is in a bitter rivalry with Hamas, which routed his forces in the Gaza Strip last year and seized control of the area.
The Israeli daily Haaretz on Tuesday criticized the government for giving Mr. Carter, a Nobel laureate who brokered Israel's first peace agreement with an Arab nation, a cool reception.
"The boycott will not be remembered as a glorious moment in this government's history," the newspaper said. "Jimmy Carter has dedicated his life to humanitarian missions, to peace, to promoting democratic elections and to better understanding between enemies throughout the world."
Earlier this week, Mr. Carter said isolating Hamas is counterproductive and volunteered to serve as a conduit between the group and the U.S. and Israeli governments.
Mr. Carter acknowledged Tuesday he was not on an official mission and had "no authority at all."
"I'm not a negotiator. I'm just trying to understand different opinions and provide communication between people," Mr. Carter said.
When meeting Mashaal, Mr. Carter said, "I'm going to try everything I can to get him to agree to a peaceful resolution," both with Israel and with Hamas' internal Palestinian rivals.
Mr. Carter said he requested permission to enter Hamas-ruled Gaza but was turned down. He did not provide details. Israel and Egypt control Gaza's border crossings and such a visit would also require the approval of Mr. Carter's U.S. Secret Service detail. There have been no official visits to Gaza by Americans since Hamas won Palestinian parliamentary elections in early 2006.
President Bush did not visit Arafat's mausoleum in Ramallah when he visited earlier this year.
Mr. Carter's office also said a request for security protection from Israel's Shin Bet agency had not been met.
The Shin Bet said it never received a request to provide security. Stewart Tuttle, spokesman for the U.S. Embassy, said the embassy never relayed a request for Shin Bet protection because Mr. Carter was on a private visit.
A statement from the Carter delegation said the former president's U.S. security detail "was always, without exception, assisted" by the Shin Bet in previous visits after he left office. However, the statement did not directly blame Israel.
Several former State Department officials who have followed Mr. Carter's efforts in the Middle East for years also see a pattern in his refusal to follow the official policy guidelines, reports Wolfson. The former president, they note, seems to have an inclination to periodically insert himself into various aspects of peacemaking in the region, a tendency which rankles some officials and others who have watched him in the years since he left the White House. Clearly, however, Mr. Carter feels his status as a Nobel Peace Prize winner and his own efforts brokering the 1979 Camp David Accords which led to a peace treaty between Israel and Egypt give him as much latitude as he wishes to exercise.