GAZA, Dec 23 (Nidal al-Mughrabi/Reuters) - The United Nations said on Thursday that Israel and the Gaza Strip's rulers, the Islamist group Hamas, had indicated they wanted to reduce tension in and around the coastal enclave and appealed for an end to hostilities.

We are hearing a clear desire from all concerned to de-escalate the situation and respect calm and I appeal for an end to acts of violence, Robert Serry, UN Special Coordinator for the Middle East Peace Process, said in a statement.

Rocket and mortar fire from Gaza have increased in the run-up to the second anniversary of Israel's devastating Gaza offensive which began on Dec. 27, 2008 and rocked the enclave for three weeks before an unofficial ceasefire.

On Thursday one Palestinian was killed and three were wounded in the northern Gaza Strip when they approached the border fence at a point Israel has declared off limits, Gaza medical officals said.

Palestinian hospital sources said the dead man was a shepherd and those wounded were another shepherd and two men sifting through rubble.

An Israeli army spokeswoman said troops had spotted four suspicious figures and shot at them when they did not heed orders to leave the area.

Gaza hospital sources said 13 Palestinians had been killed in cross-border hostilities with Israeli forces this month.

Last weekend, an Israeli air strike killed five Palestinian militants, the biggest single toll since the Gaza war two years ago in which 1,400 Palestinians and 13 Israelis died. Militants have launched at least 25 rockets into Israel in the past two days, the army said.

EFFORTS FOR CALM

Serry said he and UN colleagues were trying to help de-escalate the situation.

Israeli officials have said Israel has no wish to raise tension and will show restraint provided it is not provoked. Hamas said Israel, which carried out air strikes against militants in response to the rocket attacks, was the aggressor.

A Hamas spokesman said Ismail Haniyeh, the group's leader in Gaza, had called on UN Secretary General Ban ki-Moon to punish Israel on the grounds that it was to blame for the violence through its military actions and its blockade of the territory.

On Wednesday, after a rocket landed close to an Israeli kindergarten, Serry issued a statement condemning the firing of indiscriminate mortars and rockets by militant groups in Gaza at Israel.

The rocket attacks were in clear violation of international humanitarian law, he said, adding that Israel had a right to self-defence ... in launching air strikes that target Gaza militants.

Israel tightened its land, air and sea blockade of the Gaza Strip in 2007 after Gaza militants abducted Israeli soldier Gilad Shalit in a cross-border raid. It recently reduced restrictions on exports of goods from the territory.

More than 200 rockets and mortar rounds have been fired from Gaza into southern Israel this year. The attacks killed only one person, a Thai farm labourer hit by a mortar round in March.

Israel's air strikes at armed militants and rocket squads in Gaza have often killed their targets, and sometimes civilians.