"We are holding the soldier. He is alive and in good health," the representative of the group, speaking on condition of anonymity, told news agency AFP.
He gave no indications as to the whereabouts or the missing soldier, who was abducted during a Palestinian attack on an army border post close to the Gaza Strip on Sunday that left two Israeli soldiers and two militants dead.
The Popular Resistance Committees, together with the armed wing of the governing Hamas movement and the previously unknown Army of Islam claimed joint responsibility for the attack.
Israel has vowed to avenge any harm done to the missing soldier.
Meanwhile, an Egyptian security delegation has made contact with the kidnappers, Israeli public radio said.
The delegation, which arrived in the Gaza Strip on Sunday, established contact with the kidnappers through a third party, the radio said.
The soldier was wounded, the radio said quoting the Egyptian delegation, without giving details.
Bloodstained jacket found
The bold and well coordinated attack killed four and injured four Israeli soldiers, one of them seriously, but officials hold the most concern for the missing soldier, 20 year old Gilad Shavit. Mr Shavit's bloodstained bulletproof jacket was found close to the scene of the attack.
In a joint statement, the three militant groups say that the dawn attack was revenge for the 22 civilians allegedly killed by botched Israeli shelling and air strikes since the start of the month.
"This operation was a clear and final message to the enemy leaders: they need to keep civilians far from their hateful bullets and leave the battle between the heroes of the resistance and the soldiers," the statement said.
Israeli tanks, troops and Apache combat helicopters stormed into the area to search of the missing soldier and to investigate the tunnel used by the militants.
Strong retaliation
Israel’s Defence Minister Amir Peretz has vowed a strong retaliation if Mr Shavit is not released unharmed. "We will take revenge against anyone who injures the soldier, including their leaders."
The army chief, Dan Halutz, earlier said he believes the missing man is still alive, adding that "Hamas is involved in this matter from head to foot, literally."
Israel’s security cabinet has already approved reprisal operations against the Gaza Strip but upon the urging of Israeli Prime Minister Ehud Olmert, has delayed the operations until Mr Shavit has been returned.
Mr Olmert blamed Palestinian president Mahmud Abbas and the Hamas-led Palestinian government for the attack on the military post. The country’s Foreign Minister Tzipi Livni urged the Palestinian Authority, and its president, to quickly release the soldier, using force against the militants if necessary.
"This is an opportunity for Abu Mazen (Abbas) to prove how serious his intentions are. Israel expects him to act immediately to return the kidnapped soldier to Israel and he has the necessary military means to do so," Ms Livni said.
Hamas demands soldier’s release
The deputy prime minister of the Hamas led government, Nasseredine al-Shaer, has also demanded the immediate release of the soldier, telling a news conference, “His captors must spare his life and look after his health."
The Hamas led government had earlier said it had no information into the soldier’s kidnapping.
President Abbas, also condemned the suspected kidnapping, "We have always warned against the danger of certain groups or factions leaving the national consensus and carrying out operations for which the Palestinian people will always have to pay the price."
Meeting cancelled
Meanwhile, one on one talks between President Abbas and the prime minister of the Hamas government, Ismail Haniya, have been cancelled because of the strike on the military border post.
The talks, which followed on from discussions yesterday, were in a bid to end the power struggle between the two feuding factions.
Separately, a planned meeting of the two factions was canceled at the last minute at the request of Mr Abbas and Mr Haniya, who both wished to hammer out an agreement between themselves before presenting it their parties.
Negotiators have remained at odds over crucial points, namely acceptance of a Palestinian state based on borders in place before the 1967 Arab-Israeli war, the supremacy of the Palestine Liberation Organisation and talks with Israel