Dr. Mahmoud Zahar, a senior Hamas leader who was involved in negotiations with an aide to Prime Minister Yitzhak Rabin, said that the delay came in response to a request from jailed Hamas leader Sheik Ahmed Yassin.
"The deadline has been extended on the condition that all our demands be met," he said, after emerging from his house in Gaza City.
Zahar said that Israel must agree to release Yassin and other prisoners within 24 hours.
"If they don't, there will be negative results," he said.
A similar statement was made moments before by Raid Salah, an Israeli-Arab fundamentalist leader.
Zahar returned to reporters moments after making the initial announcement and stressed that the extension was "not free of charge," and Israel had to meet its demands if the crisis was to be defused.
Israeli government spokesman Uri Dromi said the government had no comment.
The soldier, Corporal Nachshon Waxman, 19, was snatched Sunday while hitchhiking. The abduction has snarled the peace process and spoiled the award of the Nobel peace prize to Rabin, Foreign Minister Shimon Peres and PLO leader Yasser Arafat.
Negotiations were carried out by telephone with Eitan Haber, Rabin's top political aide in Tel Aviv, and Talab al-Sanaa, an Arab member of Israel's parliament who went to the Zahar's home in Gaza.
Al-Sanaa told army radio that he had relayed a proposal to Hamas from Israel and that Hamas was studying it. An Israeli official confirmed that al-Sanaa had passed a message to Hamas from Israel but termed it "unofficial." Sufian Abu Zaide, a top Arafat aide, said he believed Hamas would yield to the demands of public opinion as well as the appeals for mercy from Palestinian prisoners and Yassin himself.
"The feeling of the Palestinian public is against the killing," he said.
But rumors were also rife in Gaza of a possible Israeli military action. The Israeli army closed one of the main entrances to the strip.
The International Committee of the Red Cross reported that a message to Israel's government was relayed from a member of Hamas' military wing, Izzedine al-Qassam, via the Red Cross office in Beirut.
The kidnappers had said Israel had to release Yassin and 200 other prisoners by 9 p.m. Friday or the soldier would be killed.
Rabin said the time has come for Arafat to choose between Hamas and continuing peace talks with Israel.
"Today, the Palestinians face the moment of truth. If they do not defeat the enemies of peace, the enemies of peace will defeat them," Rabin said in a statement issued after the Nobel winners were announced.
Arafat pledged he would make "major efforts" to find Waxman, who holds dual Israeli-American citizenship. He convened his top security officials just hours before the kidnappers' deadline Friday.
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