The radio report did not give details of the Israeli answer, which came after government officials wrapped up marathon top-level meetings early Tuesday without publically announcing whether they had agreed to accept the Gaza militants' demand to swap 1,000 Palestinian prisoners for the lone Israeli serviceman.
Sgt. Gilad Schalit has been held prisoner by Hamas for 3 1/2 years.
The fact that no further meetings were due indicated that a response had been agreed on by Israeli Prime Minister Benjamin Netanyahu and six Cabinet ministers who took part in the late-night talks.
A decision to pay that lopsided price for 23-year-old Sgt. Gilad Schalit could reshuffle Mideast politics in unpredictable ways and possibly ease a punishing blockade of the Hamas-ruled Gaza Strip.
The Israeli officials were divided heading into Monday night's talks, with some ministers opposed to freeing Palestinians convicted in fatal attacks, arguing they could kill again. Israel also wants the most hard-core prisoners deported outside the West Bank.
After more than four hours of talks, Netanyahu's office released a statement early Tuesday saying only that instructions were given to the negotiating team about "the continuation of efforts to bring Gilad Schalit home safe and sound."
As the Monday evening meeting began, Netanyahu's office issued a terse statement saying, "The prime minister will continue to protect Israel's security and the lives of its citizens as the most important factor" in a decision over the soldier.
A Palestinian close to the negotiations said a German mediator carrying a proposal approved by Hamas had set a Wednesday deadline for Israeli action. The Palestinian, who spoke on condition of anonymity because of the sensitivity of the matter, said there would be no further negotiations.
In between Monday's meetings, Netanyahu sat down with Schalit's parents, who have waged a high-profile crusade to free their son. The young tank crewman was dragged bleeding into Gaza by Hamas-linked militants who tunneled into Israel in a daring June 2006 raid, killing two other soldiers.
Schalit's father, Noam, who has had his hopes raised and dashed repeatedly, said afterward that he was neither optimistic nor pessimistic. At a protest tent outside Netanyahu's residence, about 100 demonstrators carried life-size cardboard cutouts of Schalit and urged Cabinet ministers to wrap up an agreement.
Hamas, the Islamic militant group that seized control of Gaza a year after Schalit's capture, stands to be the biggest winner if the deal goes through.
It could claim credit for the largest prisoner release in years - an achievement of paramount importance in Palestinian society, where nearly every family has had relatives in Israeli jails. A swap could also bolster the Hamas claim that only violence, not peacemaking, wrings concessions from Israel.
Hamas also hopes a prisoner exchange would ease a crippling Israeli and Egyptian blockade of impoverished Gaza. That embargo has prevented the tiny seaside territory from rebuilding after Israel's devastating offensive a year ago to stop daily Palestinian rocket attacks. Israel has said it would not consider lifting the blockade until Schalit is home.
Israel imposed tight restrictions on access to Gaza after Schalit was captured, then virtually sealed off the territory, home to 1.5 million Palestinians, after Hamas violently seized power the following year.
The big loser could be Hamas' rival, Palestinian President Mahmoud Abbas. The 74-year-old moderate leader, who governs only in the West Bank, has had little to show for years of peace efforts and could appear weaker than ever if Hamas wins the freedom of hundreds of Palestinians.
Abbas could be in even bigger trouble if Israel releases Marwan Barghouti, a popular grass-roots leader and Abbas' key challenger inside the Western-backed Fatah movement. It's not clear if Barghouti is on the list of those to be freed, but he's considered a strong contender to become the Palestinians' next president.
The Palestinian close to the negotiations said Barghouti, who is serving multiple life sentences after being convicted in fatal attacks against Israelis, would be allowed to return to his West Bank home. Hamas agreed that several other hard-core convicts would be deported, he said.
Prisoner swaps are controversial in Israel because of their potential to encourage militants to take more hostages. But the plight of the quiet, gangly Schalit and his family has touched many hearts in Israel, where military service is compulsory and families expect the army to do all it can to protect their children.
Bringing Schalit home could boost Netanyahu domestically, given the Israeli public's deep concern for the young man's fate. However, it could also hurt the prime minister's standing among Israelis who feel releasing prisoners convicted of violence would only invite more bloodshed.
Israel has balked at meeting the Hamas demand to release Palestinians convicted of particularly shocking violence, such as the bombing of a Passover celebration that killed 30 people in 2002. It also wants some prisoners deported to Gaza or overseas, rather than to their West Bank homes, on the assumption they would be less able to harm Israel from there.
Izzat Rashaq, a top member of Hamas' exiled leadership, said in Beirut on Sunday that the group was sticking to its demand that senior militants be freed. He said he was expecting to get Israel's response from a German mediator within days.
Israel and the Iranian-backed Hamas have held years of on-again, off-again swap talks through Egyptian mediators. But no dramatic progress was reported until the German mediator entered the picture several months ago.
In October, Hamas released a video of Schalit, providing the first visual evidence since his capture that he was alive. Hamas also declared last month that all of Gaza's militant groups had agreed to suspend rocket attacks on Israel, a promise largely kept.
Suleiman Awwad, the Egyptian presidential spokesman, called on Gaza's Hamas rulers to end the suffering of Palestinians, an apparent reference to the release of Schalit, as a way to removing the blockade on Gaza.
On Sunday, Iran's parliament speaker, Ali Larijani, said during a visit to Egypt that Iran was not trying to interfere in Egypt's mediation efforts - a possible sign that Iran has given a green light for a deal.