The ABC host was previewing a longer interview scheduled for Sunday's edition of This Week.
GMA co-host Robin Roberts cheered, "From the politicians hoping to make history in November, to one politician trying to make history right now."
Amanpour speculated as to whether Tea Party nominees would derail the administration's efforts in the Middle East: "Is it possible to have the President's foreign policy agenda, you know, furthered, even if a lot of Tea Party candidates do end up being the candidate [sic]?"
The anchor has a history of lauding Clinton. On May 14, 1999 , she complimented the "dignity" the then-First Lady showed during the Monica Lewinsky scandal:
"A lot of the women that I meet from traveling overseas are very impressed by you and admire your dignity. A lot of the people you meet are people who suffered, people you saw today, and who believe that they identify with you because they have seen you suffer. And in a speech in Africa last year, you spoke about living for hope and reconciliation, living for forgiveness and reconstruction, and living for a new life - have you been able to apply that to your own circumstances? Have you been able to forgive your husband?"For the full interview with the Secretary of State, see Sunday's This Week.
- CNN's Christiane Amanpour to Hillary Clinton in Macedonia after a tour of refugee camps, May 14, 1999.
To read the MRC's Profile in Bias on Amanpour, go here .
A transcript of the segment, which aired at 7:11am EDT, follows:
ROBIN ROBERTS: From the politicians hoping to make history in November, to one politician trying to make history right now. Hillary Clinton is in Israel this morning, attempting to broker a landmark peace agreement between Israel and the Palestinians. And that's where Christiane Amanpour sat down with the secretary of state for an exclusive interview. Did this just a short time ago. Christiane, so good of you to join us this morning from Jerusalem. And is Hillary Clinton making any progress?-Scott Whitlock is a news analyst for the Media Research Center. Click here  to follow him on Twitter.
CHRISTIANE AMANPOUR: Good morning, Robin. She says yes. All the officials say yes, including the participants, Benjamin Netanyahu and Mahmoud Abbas. Apparently they've gotten down to core issues already. And they're doing that in a serious way. But, the huge ten-ton elephant in the room is the looming end to Israel's moratorium on settlement building. I asked Secretary Clinton if there's any progress, any flexibility towards keeping the moratorium on? She wouldn't go into specifics, other than to say the two sides must stay at the table. There is this moratorium that's looming on the horizon. Are the talks going in a constructive way?
HILLARY CLINTON: Yes. I would say they're in a constructive channel. And that has been, you know, very reassuring to us.
AMANPOUR: President Obama has said that given the talks going in a constructive way, there should be- Israel should continue the moratorium on settlements. Do you believe that will happen?
CLINTON: Well, that certainly is our hope. Now, we've also said that we'll support an agreement that is reached between the parties. It took a lot of political capital for Prime Minister Netanyahu to achieve this moratorium. It had never been done before. At the same time, it's been in effect for the time it was set for. And the talks are just starting. So, we are working hard to make sure there remains a conducive atmosphere to constructive talks.
AMANPOUR: While nobody will confirm exactly what might be flexibility, we're hearing that there may be an extension or there may be calls or an extension of the moratorium for about three months or so. In addition, Secretary Clinton is now on her way to Jordan, where she will meet with other Arab leaders, such as King Abdullah of Jordan on this issue, Robin.
ROBERTS: But, back here at home, a lot of talk about the Tea Party. I know you asked the secretary about that, too.
AMANPOUR: I did. She refused to talk politics. She said, "I'm not in that anymore." But she did say, when asked how would some of these candidates, if they become senators or representatives, affect U.S. foreign policy, this is what she had to say. Is it possible to have the President's foreign policy agenda, you know, furthered, even if a lot of Tea Party candidates do end up being the candidate [sic]?
CLINTON: Well, I've seen a lot of people run for office and say a lot of things. And then, when they have the burden of holding office and the responsibility that goes with it, I've seen them become very sobered very quickly about the challenges that we face domestically and internationally. You know, nobody said it better than Mario Cuomo when he said, "You campaign in poetry and govern in prose." And, you know, sometimes the poetry can get hot and a little over the top. But the prose brings you down to earth.
AMANPOUR: And of all of the things you have undertaken over the last several months, was your daughter's wedding- where does that fit in there? And hard? Difficult?
CLINTON: It was the most wonderful experience. But, as I confessed leading up to it, it was stressful. I think being a mother of the bride is stressful under any circumstances. Doing it long-distance, jet lagged, on planes, in the midst of diplomatic negotiations, made it a little more so.
AMANPOUR: Now, negotiators are still, now talking about another meeting for when to get the principals together. We don't know when that will be. But we know it will be soon.
ROBERTS: I know you had a wide-ranging conversation with the secretary. Christiane, thank you so much. Safe travels. We'll see you soon. And Christiane will have much more on her conversation with the secretary. And also is going to sit down with the Iranian President, Ahmadinejad. And you'll see it all on This Week, Sunday morning.
GEORGE STEPHANOPOULOS: You know, I think doing the seating at that wedding would rival putting together Middle East peace.
ROBERTS: I think she's on to something there.