RAFAH, Gaza Strip (Reuters) - After years trapped in the noisiest, most devastated flashpoint of conflict with Israel, Palestinians are sleeping nights again.

It didn´t take much for new President Mahmoud Abbas to be a hit in Rafah.

"The constant din of gun battles has finally stopped. For us, that´s progress," said Hamed Qeshta in Rafah refugee camp, a vast slum partially razed into the desert sand by the Israeli army in four years fighting Palestinian militants.

Relative calm has dawned since Abbas won election as Yasser Arafat´s successor on a platform of peaceful struggle for statehood and cajoled militants into a tacit truce. Israel has answered by curtailing military action.

That does not mean bloodshed has stopped.

On Monday, the killing of a girl at a school near the no-go border zone prompted a retaliatory mortar salvo at Jewish settlers by militants -- though Israel denied responsibility and blamed gunfire by Palestinian revelers for her death.

The day before, Israeli troops shot dead an elderly Rafah man they said had entered a forbidden area.

The incidents shook Rafah, but did not dash hope that things are changing for the better.

"These deaths obviously make us nervous about a relapse. But really, the atmosphere is so much quieter on the front line here," said Qeshta, from a large Rafah clan.

Residents from all walks of life, those clinging to homes on the edge of the rubble, a city official, hardened militants and an executive of Gaza´s shuttered airport all say: Let´s keep things quiet to give Abbas a chance.

To popular acclaim, Palestinian police have resurfaced under Abbas´s orders to safeguard the truce and rein in armed gangs. And the militants are cooperating for now after Abbas promised he would try to integrate, not crush, them as Israel prefers.

ABBAS CAN´T AFFORD TO REST ON EARLY LAURELS

But everyone warns Abbas must do more and fast to prevent a return to violence.

He is under pressure to end years of economic meltdown and start negotiating for a total Israeli pull-out from occupied lands. Israel intends to quit Gaza this year, but aims to hold onto significant chunks of the West Bank forever.

"Arafat was a legend, a man of revolution. But people see Abbas as a man of practical steps who must earn our trust that way," said Omar al-Naqa, a senior aide in Rafah municipality that is run by Abbas´s Fatah movement.

The killings of the old Rafah man and schoolgirl infuriated militants, but apart from firing off a few mortars they insisted they were committed to restraint in support of Abbas and would not go beyond "one-off responses."

"We want to stay calm since this is the people´s wish," said Abu Ibrahim, 31, a militant commander with a luxuriant black beard, piercing gaze and submachine gun close to hand.

"But we give Abbas at most a few months to start delivering. If not, we will have nothing to lose. We will return to arms."

GUNMAN VENTURE OUT

With Israel´s announced halt to assassination and arrest raids, Rafah gunmen now dare brief outings by day while still sleeping in different places every night.

Abu Ibrahim of the al-Aqsa Martyrs´ Brigades, a Fatah offshoot, spoke softly in a car parked amid fields to give bodyguards a clear view.

Then his cell phone rang.

"It´s my wife. I must go visit the children now. But I still can´t move back in -- too dangerous for them," he said.

After years of deepening poverty, isolation and decay, the 1.3 million Palestinians crammed into tiny Gaza are desperate for jobs and trade. On Rafah´s outskirts soars a silent monument to economic potential -- Gaza International Airport.

Arafat ordered the colonnaded stone and marble complex built in the heady period after 1990s interim peace deals, only to see its runway torn up and radar stations bombed by Israeli forces in 2001 after statehood talks collapsed into bloodshed.

There have been no flights since.

But Zakariya al-Mahran, the airport´s dapper deputy manager, never stopped coming to work, keeping the terminal tidy and well maintained with skeleton staff. With the rise of Abbas, Mahran hopes his lonely vigil will finally pay off.

Toying with an Israeli helicopter cannon shell that has become an ornament on his desk, he said a Turkish delegation was due in late February to assess runway and radar repair costs and Germany had offered to help foot the bill.

"Every new country needs an airport to connect with the outside world," he said. "God willing, Abbas will preserve the calm so we can reopen here and get Gaza off the ground." (© Reuters 2005 02/03/05)