The death toll in Nepal’s devastating earthquake may go up to 10,000, Prime Minister Sushil Koirala on Tuesday told the envoys of India, China and the US.

Koirala told the ambassadors that nearly 4,400 people were already dead from Saturday’s temblor, many of the thousands of injured were in serious condition and further hundreds were missing across the country.

All these put together may push up the death toll to 10,000, Koirala’s media advisor Prakash Adhikari told IANS, quoting what the prime minister had told the envoys of the three countries.

Koirala’s assessment would make this worst ever earthquake to hit Nepal.

Koirala also sought more and quicker international aid to provide both immediate assistance to the earthquake victims and to rebuild the country.

Even as international aid pours into the country, overwhelmed hospitals are lacking vital medical supplies, and rescuers are struggling to reach hard hit rural areas near the quake’s epicenter.

“The biggest problem is reaching these villages,” Matt Darvas, an emergency communications officer for the humanitarian group, told CNN from Gorkha district, northwest of the capital, Kathmandu.

The death toll in Nepal stood at 4,352 Tuesday morning, according to the country’s Home Ministry. Another 72 people died in India, while China reported 25 deaths.

Most of the casualty numbers in Nepal are believed to have come mainly from Kathmandu and the surrounding area. They are expected to rise further as information emerges from more remote areas.

Four U.S. citizens are among the dead, according to the State Department.

The United Nations estimated that the disaster had affected 8 million people across the Nepal. More than 1.4 million people are in need of food assistance, the world body said in a situation report Monday.

UNICEF, the U.N. children’s agency, said Sunday that nearly 1 million Nepalese children urgently need assistance.

Numerous aid groups and at least 16 nations rushed aid and workers to Nepal, with more on the way.

And across the region, tens of thousands of people spent another night outdoors, fearing that damaged buildings could collapse in the event of more aftershocks.

With inputs from CNN/IANS