MUZAFFARABAD, Pakistan (AP) – One month after South Asia’s Oct. 8 earthquake, the estimated death toll shot up sharply to 87,350 on Tuesday following a new count of Pakistan’s casualties, an official said.

The United Nations again appealed for more money to help victims, urging donors to be as generous as with other recent disasters. The world body said it urgently needs $42 million to maintain the aid effort through November.

But U.N. officials in Pakistan said they were cautiously optimistic that a humanitarian catastrophe could be avoided.

The toll in Pakistan jumped to 86,000 – or 13,000 higher than the government’s official toll – under a broad assessment by the World Bank and Asian Development Bank, working with local governments and aid agencies, Pakistani Finance Ministry official Iqbal Ahmed Khan said Tuesday.

India has reported 1,350 deaths in its portion of divided Kashmir.

Khan said the new tally for Pakistan came after more bodies were pulled from debris and recovery teams reached areas previously blocked by landslides unleashed by the magnitude-7.6 quake and its hundreds of aftershocks.

“This is their assessment, which we think is fair enough,” Khan said. “They had various teams in the field. This is feedback from the field.”

The central Pakistani government’s official death toll – still at 73,000 – typically has lagged behind other tallies, including those of local provincial governments in the quake-affected areas, whose most conservative estimates have added up to 79,000 for Pakistan for more than two weeks.

Aid officials fear that winter could bring a new wave of deaths among survivors, from hypothermia and respiratory illnesses such as pneumonia.

“We are very anxious about when the snow falls,” said quake survivor Hafiz Mohammed Aslam, a preacher in the village of Kotramaskhan in Pakistan’s portion of Kashmir. “It will become a terrible situation, especially for the children.”

The U.N. humanitarian chief Jan Egeland said Monday in New York that people in Kashmir could “freeze to death if they don’t get assistance in weeks,” urging everyone from individuals to oil-rich nations to be as generous as they were with other recent natural disasters.

However, at a news conference Tuesday in Islamabad, U.N. aid officials indicated that funding and the efforts of aid workers have begun to catch up with the needs.

“Perhaps for the first time since Oct. 8, there is a sense of cautious optimism in the humanitarian community,” said local U.N. emergency coordinator Jan Vandemoortele. “The job is colossal, but there is a feeling that this is a doable job. It is not mission impossible.”

The U.N. officials made no mention of scaling back helicopter aid flights, as they had warned about doing in recent weeks unless more funding came through.

The U.N. said it has received about $85 million of the $550 million it has asked for, with about $49 million more pledged. More than $40 million is needed immediately to get through November, the U.N. Office for the Coordination of Humanitarian Affairs said Monday from Geneva.

The quake destroyed the homes of more than 3 million people across Pakistan’s North West Frontier Province and its portion of Kashmir, many of whom have moved into the many tent camps that have been set up in foothills of the Himalayas.

The U.N. has launched “Operation Winter Race” to shelter to about 200,000 people living at high altitudes above the snow line in the rugged Himalayas and about 150,000 expected to come down to tent camps at lower elevations.

Tents already pledged and in the pipeline should take care of those people, Egeland said.

Survivors continue to stream into the Kashmiri Pakistan hub of Muzaffarabad, where they pick up tents from aid agencies before trudging out of town with canvas and poles on their backs in search of any flat ground not already claimed by other survivors.

Some can be seen trekking along the Neelum River up to windy bluffs overlooking the city, where they must dig into the slope with crowbars to carve a shelf big enough to pitch a tent.

“Life is very difficult,” 28-year-old survivor Jamil said in the Pakistani Kashmir hub of Muzaffarabad as he hauled a freshly donated tent up to a cold mountainside camp. “I waited one month for a tent and our food doesn’t last long.”

Also Tuesday, about 200 supporters of Pakistan’s largest Islamic group, Jamaat-e-Islami, rallied in Muzaffarabad to protest the detention by police of a member at a relief camp for earthquake survivors. Police on Monday picked up Jamaat-e-Islamic activist Shamsher Khan during a raid on the relief camp he runs for quake survivors but released him about five hours later, said deputy police chief Atta Ullah.

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