Ehud Olmert, the acting Israeli prime minister, approved the meeting, Olmert's office said on Monday.
Olmert's office said the topics of the meeting were economic. Abbas aide Nabil Abu Rdeneh gave the same description in a phone call from Vienna, where Abbas is holding talks.
The secret talks between Abbas and Peres, a key Olmert ally in the new Kadima Party, came two weeks before Israel's election, set for this month. Kadima has a wide lead, but Olmert has been taking steps to stem a drop in support.
The Peres-Abbas meeting apparently was meant to attract the support of moderate voters. Peres is a former leader of the dovish Labour Party and an architect of interim peace deals with the Palestinians.
Olmert breathed life into a sleepy election campaign over the weekend when he spelled out his plans for the West Bank - saying he would withdraw from significant parts and move settlers from outlying locations into settlement blocs Israel would keep.
Abbas (L) has invited Haniya to
form a government
He said he preferred peace negotiations, but with Hamas in control of the Palestinian government, he was prepared to move unilaterally.
Likud leader Benjamin Netanyahu said Olmert has transformed the election into a referendum on the future of the West Bank.
Peres and other doves have insisted that despite the Hamas victory, Israel must maintain contact with Abbas, head of the Fatah Party defeated by Hamas in the parliamentary vote.
Abbas was elected president of the Palestinian Authority in January 2005 and has three years left to serve, regardless of the makeup of the parliament or cabinet.
In Gaza, Hamas negotiators met through the day on Monday with leaders of other Palestinian factions. Hamas has until the end of the month to form a government.
Since it has an absolute majority in the parliament, it could go it alone, but Ismail Haniyeh, the incoming prime minister, has said he wants as broad a government as possible, even including Fatah.
However, its platform is likely to keep Fatah on the sidelines. Hamas officials have said they favour continued resistance to Israeli occupation as a legitimate right, refusing to renounce violence, and they decline to endorse the interim peace accords with Israel, signed by Fatah.
Israel has cut the transfer of tens of millions of dollars a month in taxes and customs, and Western donors are considering how to support the Palestinian people without financing Hamas.
Israel, the US and European Union list Hamas as a terror group.
Hamas justifies its attacks as an eye-for-an-eye policy, claiming they are retaliation for Israel's occupation and attacks on civilians in the occupied territories.
Hamas has launched no attacks in the past year during a cease-fire.