The first meeting, held after a day of US-sponsored peace talks in Annapolis, also ended in discord on December 12.
The two sides reportedly agreed that Ehud Olmert, the Israeli prime minister, and Mahmoud Abbas, the Palestinian president, would meet in the next few days, although no specific date was agreed upon.
The meeting's failure comes as Israel's cabinet delayed a decision on easing the country's requirements for releasing Palestinian prisoners.
The easing of restrictions would clear the way for a deal to win the release of Gilad Shalit, an Israeli soldier captured by Gaza fighters last year.
The decision will reportedly be delayed until later this week, officials from Olmert's office said.
Also on Monday, Tzipi Livni, the Israeli foreign minister, said that Israel had done a "terrible job" of stopping arms smuggling into the Hamas-controlled Gaza Strip, an Israeli parliamentary spokesman quoted her as saying.
Israel has long complained that Hamas smuggles weapons through tunnels at the border between the Gaza Strip in the so-called Philadelphia corridor that separates the two.
Between 1967 and 1977 Israel constructed 30 settlements with more than 5,000 settlers, mostly in West Bank
Israel pulled out of all 17 Gaza settlements and four West Bank settlements in August 2005
About 440,000 settlers remain in the West Bank and East Jerusalem
Settlements cost the eli government about $556m each year
Israel's sparation wll around the pied West Bank will stretch for more than 700km, looping around most settlements
Based on the current plan, 8.6 per cent of the West Bank falls on the Israeli side of the wall
Sections around Ariel and Maale Adumim settlements are the most contentious as they cut deep into the West Bank, dividing it from East Jerusalem
Source: Peace Now
At the first round of talks on December 12, Abbas demanded Israel drop plans to build 300 new homes in an area near Jerusalem known to Israelis as Har Homa and to Palestinians as Abu Ghneim.
On the eve of the second round of negotiations, Israel's construction ministry unveiled a proposal to build 740 new homes next year on occupied land near Jerusalem.
Of them, 500 would be in Har Homa and 240 in the Maale Adumim settlement.
Abbas said he could not understand why Israel was "carrying out frenzied settlement activity during final status negotiations".
Mark Regev, spokesman for Olmert, said Israel would meet its obligations.
He said Israel would not allow "outward growth" of existing settlements by preventing new settlements from being built, and by not confiscating any more Palestinian land.
But Israel will allow construction within built-up areas of existing settlements, he said.
Israel wants to keep Maale Adumim and other large settlement blocs in any peace deal.