The ceasefire resolution approved unanimously last week by the UN Security Council did not demand that Hezbollah release two Israeli soldiers whose capture sparked the conflict, nor did it demand that Israel release Arab prisoners.
However, in the preamble to the resolution, the council said the situation should be addressed urgently.
Jackson said he spoke to Daniel Ayalon, the Israeli ambassador, and appealed to his government to consider "some exchange of prisoners" as a goodwill gesture "if there is movement on the two abducted Israelis", Jackson said.
He then called on Iyad Moustapha, the Syrian ambassador, whose government has strong ties to Hezbollah.
"We are negotiating with one hand tied behind our back -we talked to Russia through the height of the Cold war"
US civil rights activist
"I asked him to make an appeal to his president, Bashar Assad, on a humanitarian basis to appeal to whoever is appropriate, maybe Hezbollah, to seek the whereabouts and grant the release of the two Israeli soldiers," Jackson said.
"He was positive and said he would convey the message."
Although Jackson said he could not find out about the health of the prisoners, he said he had the impression they were "all right".
Jackson said he and other religious leaders would go to Syria "if we had the notion [and] could gain the release of prisoners on both sides".
"Such an effort would not be in conflict with our present policies because it would be humanitarian," he said.
However, Jackson said the US should be talking to Syria and to Iran, which it accuses of being the principal source of Hezbollah's weapons.
"We are negotiating with one hand tied behind our back. We talked to Russia through the height of the Cold war," he said.
Justin Higgins, a US state department official, said that Jackson's talks with Syria and Israel were undertaken as a private individual.
On several occasions, Jackson has successfully intervened on behalf of Americans and others held hostage or prisoner in foreign lands.
In January 1984, he met Hafez Assad, president of Syria at the time, and arranged the release of a US navy pilot whose plane had been shot down over Lebanon during an US air strike against a Syrian anti-aircraft position a month earlier.
Later that year, Jackson travelled to Cuba and persuaded Fidel Castro to release 48 US and Cuban political prisoners.