(CNN) -- Former President Carter met Friday with a top Hamas politician, exiled leader Khalid Meshaal, in Damascus, Syria, Carter aides said.
Former President Carter says he hopes to see a breakthrough in the Mideast peace process in his lifetime.
Carter, Meshaal and lower-level officials had a closed-door meeting that lasted more than an hour and a half.
The ex-president's visits with top Hamas officials this week have drawn condemnation from the U.S. and Israeli governments. They said Carter is engaging in diplomacy with a group they consider a terrorist organization.
Carter's controversial tour of the Middle East included a meeting Thursday in Cairo, Egypt, with two other senior Hamas politicians.
"I'm not a negotiator. I'm just trying to understand different opinions and communicate, provide communications between people that won't communicate with each other," Carter said at the start of his trip.
Most Israeli officials have refused to receive Carter during his visit to the region, angry over his insistence that Israel should talk to Hamas. Many Israelis dislike Carter's observations about Israeli policies toward the Palestinians in his 2006 book, "Palestine: Peace Not Apartheid." Watch as Carter makes a provocative move for peace »
U.S. and Israeli officials said they believe that Carter's talks with Hamas will achieve little and even could harm the Middle East peace process.
"Regrettably, Hamas will try to take political advantage of this," David Welch, assistant secretary of state for Near Eastern affairs, said Friday. However, he added, "I think President Carter's sincere. This man worked hard on peace."
At a State Department briefing Friday in Washington, spokesman Sean McCormack said, "I don't think people are going to confuse the efforts of a private citizen ... with the very clear policies of the United States government."
U.S. National Security Adviser Stephen Hadley said earlier, "We think it is not useful for people to be running to Hamas at this point and having meetings with Hamas."
But those who, like Carter, have spent their careers trying to make peace have another view.
"You should never give in to the terrorists; you should never accept their demands, but you should never be the ones refusing to talk," said Jonathan Powell, who was chief of staff for former British Prime Minister Tony Blair.
In more than a decade in his job, Powell supported a secret channel of communication to sworn enemies in the Northern Ireland conflict. He said it was the only way to make peace.
"Any democratic government finds it very, very hard to talk to people who are killing their people. It is a very difficult thing to do," Powell said. "But my argument is that you have to have that contact unless you believe that in some way, it's going to be solved militarily."
For the Israelis, a military solution is an elusive one, but they insist that talks with Hamas won't bring peace in the Middle East conflict.
"Hamas is conducting war against the citizens of Israel," said Ron Prosor, Israel's ambassador to Britain. "What do you say to people who say, 'Why don't you talk, try and talk, and not to shoot'? It sounds very good, but the question is, at what stage do you do that?"
Diplomats and statesmen frequently wrestle with the issue of whether talking with adversaries means giving in to them.
Afghan President Hamid Karzai has said that his government has had discussions with the Taliban.
"We are willing to talk to those of the Taliban who are not part of al Qaeda or the terrorist networks," Karzai said last fall.
Nevertheless, Karzai then expelled two foreign diplomats for talking to the Taliban.
Carter, who helped broker the historic peace agreement between Egypt and Israel in the late 1970s, has said he's on a "study mission" to support peace, democracy and human rights in the region.
"It's my dream and my hope that someday in my lifetime, hopefully this year, we'll see a major breakthrough," he said. E-mail to a friend
CNN's Paula Newton and Brent Sadler contributed to this report.