The United States said Monday it is sending $10 million in relief to help the victims of the massive earthquake in Nepal, where the death toll surpassed 4,000, including at least four Americans.

The Pentagon also ordered about 24 US Army Green Beret commandos who were already in Nepal on training missions to join in rescue efforts, officials said.

Some of the Green Beret special forces troops -- who were in Nepal for high-altitude training -- are helping to search for victims "along popular trekking routes" including the Mount Everest base camp route, spokesman Colonel Steven Warren told reporters.

With fears rising of food and water shortages, US Secretary of State John Kerry and Pentagon chief Ashton Carter announced the latest details of the American aid effort, including a second military cargo flight to ferry rescue workers to Nepal.

A C-17 Globemaster aircraft traveling from Dover Air Force Base in Delaware was carrying more than 50 search and rescue specialists from the Los Angeles County Fire Department, officials said.

With that second flight, the United States would have "a nearly 130-person disaster response team" on the ground "to conduct assessments, coordinate the humanitarian response and provide search-and-rescue capabilities along with 45 tons of cargo," State Department spokesman Jeffrey Rathke said.

A previous C-17 flight left on Sunday.

Kerry offered his "deepest condolences" to the victims of the disaster in Nepal and across the region, adding "the images that everybody has seen are gut-wrenching, extraordinary devastation.

The State Department confirmed that four Americans "in the Everest region" were among the dead.

Speaking at a joint press conference with Kerry in New York, Japanese Foreign Minister Fumio Kishida said Tokyo was also sending some $8 million in aid to Nepal and had deployed 110 emergency workers.

"Tragedies of this magnitude really underscore that in today's world, next door is really everywhere," Kerry said.