Israeli and Palestinian leaders are to meet later for another session of peace negotiations in Jerusalem, but disputes have overshadowed the planned talks.
The leaders agreed to meet often to keep up progress in talks
Palestinians were angered by comments from Israel's prime minister that talks on the status of Jerusalem had been set aside until the end of the process.
"Jerusalem is a fundamental issue and cannot be postponed," said Palestinian presidential adviser Nimr Hamad.
In Gaza, Israeli troops shot dead a Palestinian militant planting a bomb.
An Israeli army spokesman said he had opened fire on troops from across the border fence in central Gaza.
On Monday, Israeli officials criticised the visiting UN humanitarian chief John Holmes, who recently urged Israelis and Palestinians to end what he called "the cycle of violence" between them.
The Israeli foreign ministry said his comments equated "terrorists" with those who were defending themselves against terror.
Israeli Prime Minister Ehud Olmert has said Palestinian leader Mahmoud Abbas had consented to hold off discussing any possible division of Jerusalem until the end of the negotiating process.
Correspondents say such a move could help the Israeli leader hold together his fragile coalition government which contains elements which adamantly oppose ceding any land in the city, whose eastern half Israel has occupied since 1967 and heavily colonised.
Speaking on Sunday, Mr Olmert stressed that Mr Abbas had "accepted" his suggestion - although Palestinian officials denied this.
Mr Abbas and Mr Olmert promised at a US-hosted peace conference in November that they would meet frequently to help negotiate the establishment of a Palestinian state this year.
There does not appear to have been any progress towards a solution since then.
Militant activity in Gaza and Israeli plans to build hundreds more homes for settlers in East Jerusalem, may have made talks more difficult.
In addition, an Israeli human rights group, B'tselem, has said Israel has imposed tough new restrictions on the movement of Palestinians in the West Bank.
B'tselem said new Israeli army roadblocks were cutting off northern parts of the West Bank and disrupting daily life for tens of thousands of people.
Palestinian Prime Minister Salam Fayyad has said the pace of negotiations must be quickened or an agreement will not be possible.
Mr Fayyad said the two leaders would "take stock of where we stand" during Tuesday's meeting.
Jerusalem is among the thorniest issues in peace talks. Palestinians want East Jerusalem to be the capital of their state, but Israel claims exclusive sovereignty over the whole city.