The Israeli Government has rejected accusations by the Palestinians that the release of more than 300 Palestinian prisoners is nothing more than a public relations exercise to please the Americans.
Despite the surrounding controversy the prisoners were clearly jubilant
The Israeli Interior Minister, Avraham Poraz, told the BBC that the releases would continue, in recognition of the progress made by the Palestinian Prime Minister Mahmoud Abbas, also known as Abu Mazen, in reducing violence.
But Mr Poraz emphasised the importance of maintaining the current ceasefire, and of making progress in peace talks.
There were emotional scenes in the West Bank and Gaza Strip as the 340 were freed - but some Palestinians said the number was insignificant, as 6,000 remain in jail.
Prisoners flashed victory signs and kissed the ground as they were reunited with relatives in the West Bank and Gaza.
Those released had either been held without trial or convicted of offences such as throwing stones at Israeli soldiers; none was a convicted killer.
Man of peace
Speaking on the BBC's Newshour programme Mr Poraz said that the goodwill gesture had been made in order to boost the position of Abu Mazen.
"We have seen since he's been in power that he was capable of stopping the terrorists, not totally, but partially and we have a sort of ceasefire right now," he said.
"I think that he is a man that wants peace - we can't say that about Arafat," he added.
Israel has said it will release another 100 prisoners later on.
"If the ceasefire lasts and we see that the peace process is once again on the road then of course we will be able to release more Palestinian prisoners," Mr Poraz said.
Militant groups such as Hamas and Islamic Jihad have condemned the releases as a publicity stunt.
Senior Hamas leader Abdel-Aziz al-Rantissi said the releases were a "drama" staged by Israeli Prime Minister Ariel Sharon for the cameras.
"If Israel doesn't release all prisoners this will destroy the hudna (truce)," he told French news agency AFP.
Even some of those released agreed with this sentiment - freed prisoner and Hamas member Mohammed Abu Daher, said the releases were "a big trick from the Israeli occupation".
The dispute has become one of the main obstacles blocking progress with the US-backed roadmap peace plan, even though the issue of prisoner releases is not part of its terms.
The BBC's James Rodgers in Gaza says setting the prisoners free is supposed to be a confidence-building measure, but it may have the opposite effect.
Many Palestinians are angry that the number of those released falls short of the 540 prisoners Israel pledged to free last week.
Nabil Abu Rudeina, a spokesman for Palestinian leader Yasser Arafat, also said the releases were "not enough".
183 people convicted of helping militants or engaging in violence against Israel
At least 139 held without charge
Nearly 100 others charged with criminal offences or entering Israel illegally
"Israel has retracted from its agreements with the Palestinian side," he said. "This step does not represent progress. We want the release of all the prisoners on a fixed timescale."
Some Israelis are dismayed that the release is going ahead at all.
Yuval Steinitz, chairman of the Knesset's foreign affairs and defence committee, said past experience suggested that the releases were a mistake.
"We released thousands of terrorists immediately after Oslo in 1993 and 1994," he said.
"And in 1995 terrorism began to escalate, including suicide bombing terrorism. Let's hope that this time it will be different."
As the prisoner releases got under way, Israel sent tanks into the West Bank city of Jericho in the first large-scale foray into Palestinian territory for several months.
At least 10 Palestinians were detained, French news agency AFP quoted witnesses as saying.
It is the first large-scale foray into Palestinian territory since Palestinian militant groups declared a ceasefire in June.
Israel has expressed concern that militants are using the truce as an opportunity to strengthen and rearm following intensive operations against them by Israel over the past few months.