There have been numerous reports of foreign aid getting stuck at Kathmandu's small international airport or even turned back at the border with India by customs officials.
"I was extremely concerned to hear reports that customs was taking such a long time. I was able to raise this with the prime minister this morning," Amos told AFP at the end of a visit to Nepal after a 7.8-magnitude quake that has killed thousands and left many more homeless.
"He has undertaken to ensure that happens, so I hope that from now we will see an improvement in those administrative issues."
Nepal's government has faced criticism for the slow pace of relief efforts, with many remote communities yet to receive any aid a week after the quake struck.
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The country's only international airport has also struggled to cope, with flights carrying aid being turned away because there was no space to park the plane.
But she said much more needed to be done to reach quake victims in remote mountainous areas of Nepal, already one of the world's poorest countries even before the quake struck.
Some 6,700 people are known to have died in the quake so far.