Jackson, who is meeting political and religious leaders in the Middle East as the head of a 10-member ecumenical delegation, also held talks with Bashar al-Assad, the Syrian president, and Hamas leader Khaled al-Meshaal in Damascus.
Jackson is a veteran at mediating between warring parties. During a 1990 visit to Baghdad when Saddam Hussein was president, he managed to secure the release of 700 foreign women and children after the Iraqi invasion of Kuwait.
He has also made successful mediation efforts during the conflict in the former Yugoslavia and in Cuba, where he convinced Fidel Castro to release 48 political prisoners.
Aljazeera.net: What was the purpose of your trip?
Jesse Jackson: There are four areas of focus. Firstly is to expand the ceasefire, because there are some who want round two [of the war]. We want the ceasefire to hold.
Secondly to get the UN troops in and to support the [UN Security Council resolution] 1701, and there is the issue of the [Israeli] sea and air blockade. Fourthly, the issue of those who are held captive.
They are four dimensions of those captives. There are the three Israeli soldiers but there are also some Syrians which is of interest to Syrian President Assad, there are some Lebanese that Hezbollah has interest in, and there are some Palestinians that Hamas is interested in. So it's a four-legged stool.
Who have you been meeting on your tour? How much progress have you made in talks?
I met President Assad last Sunday for two hours and then we met in private for two hours more on Sunday night. I was appealing to Syria to play a role in these four concerns. President Assad expressed his commitment to support our mission.
That night we met with the head of Hamas [Khaled Meshaal] in Syria. It was a very significant meeting it lasted much of the night. He said the Israeli prisoner in Gaza [Gilad Shalit] was alive and he is concerned with a swap of a thousand people at least and about the Palestinian elected officials who have been arrested [by Israeli forces].
We met with Lebanese President Emile Lahoud and Lebanese Prime Minister Saniora; we met with [Minister of Energy Mohammed] Fneish, the member of the cabinet, to get their interest, their concerns.
We met with the Israelis we met with [former Israeli prime minister] Shimon Peres, we met with the families of the prisoners, we met with the religious leaders.
Are you optimistic that you can negotiate a prisoner swap?
I don't know, I am hopeful. I do know that the longer they are held here the more they become a magnet for round two, not just a bargaining chip.
I do know that the two prisoners have been a tremendous burden for Lebanon, which bears the burden of them being here. Lebanon will be the victim if tensions re-escalate. It stands to reason for me that Hezbollah with minimum action can get maximum results.
What I heard from Fneish and Meshaal is their support they have for this. What's clear on the Israeli side is that they want verification of some physical status, some life signs that the soldiers are alive.
We asked the Hezbollah leader for a sign of life through the Red Cross or maybe by video. They tend to want the whole of this status issue as a negotiating tool.
The reason I appeal to them to show a sign of life is because it will jumpstart discussions.
I am convinced that the longer they are held, they cease to be a bargaining chip and become a pretext for expanding the second round of violence, because there are those who feel that Israel stopped too quickly [its Lebanon offensive]; that the error was not in the assumption of the war but in the tactics.
I think that negotiating releasing the captives would defuse that second round and reduce tensions.
Do you think US foreign policy has played a sufficient role in stopping this conflict? Do you think the Bush administration should increase its diplomatic efforts?
One of the great tragedies is that American foreign policy is being exposed as weak, because by not talking it has eliminated its capacity to help determine the outcome.
There is no talk with Iran, no talk with Syria or Hezbollah or Hamas. These states who are getting involved are trying to gain the advantage of an alliance with Iran for example.
Syria is too big a force to be isolated, Syria shares borders with Iraq, Syria has Iraqi refugees, Palestinian refugees, Lebanese refugees, and it's too strategic to be isolated.
The US is locked into dead-end diplomacy. It is pre-conditions for talks that will not allow talks. You should talk unconditionally. But if you don't talk you cannot enforce the outcome, so the US has opted for the sideline.
On the basis of the meetings that you have had with leaders how optimistic are you for prospects of peace in the region?
I think most of people have been devastated. People lost lives and money and credibility and strength. Round two could be even worse and could move closer to Syria and Iran which would mean World War Three, so the stakes are so terribly high.
I think that if negotiations opened up if the two [prisoners] are released and if there was enough global pressure. Israel would win; Hezbollah would win so all of those are very crucial signs.
What about other US foreign policy issues? What are your views on the US-led occupation of Iraq?
The presence of US soldiers is a magnet for the continuation of the war. America's presence becomes a cause celebre. After all, America is there as an occupying force so we could have the whole region in flames over our presence.
We are not seen as saving Iraq from Saddam Hussein we are seen invading and occupying Iraq for our own agenda and this is being deeply and violently resented though out the entire region.
We went there on the pretext of protecting America from imminent threat ... weapons of mass destruction and al-Qaida connection we didn't find that. Then we shifted the mission from saving ourselves from threat to saving Iraqis from Hussein and for democracy.
We shifted our mission and it's odd when you fight a war of this sort for democracy in Iraq and then not recognise the political parties of Hezbollah and Hamas. This is a real contradiction.
Are you concerned about the state of civil liberties in the US?
The war has been a pretext to reduce civil liberties and basic freedoms. You have warlike powers, which mean you suspend freedoms. Then they plan wars based upon an unsound assumption. We have lost money, like $250 million a day, lives, between 2000 and 3000 Americans and 50,000 plus Iraqis, we have lost honour.
America came out of World War II as the most revered nation, as the saviour of people from fascism and occupation. Then we became seen as the aggressor, we bombed Grenada, bombed Panama there was pre-emptive strike in Iraq and the Kyoto treaty.
Within the American public there is some tension. The greatness of America is that you have the right to fight. We have the right to protest, the right to vote and come [November's midterm] elections you might see some real protest at the polls.
This election in Connecticut [which saw the ousting of pro-Iraq war Democrat Joe Lieberman] - this represents a very fundamental change. This is very important. We are revisiting how we view the world community and how it views us.