DHAKA, Bangladesh (CNN) -- The first sign of survival came when recovery workers heard an iron rod strike against the massive rubble of the nine-story building outside the capital of Bangladesh, a fire service official told reporters at the site.

"I'm alive!" a woman's voice said as workers approached the basement 16 days after the building had collapsed and 10 days since rescuers had given up searching for survivors. "Please rescue me."

That account came from Capt. Ibrahim Islam, a Bangladeshi military official outside the recovery operation.

"I told her, mother don't be afraid, we are here to rescue you. ... Would you like to drink water?" Lt. Col. Moazzem Hossain said, according to Bangladesh Sangbad Sangstha, or BSS, the state-run news agency.

The use of heavy machinery was ordered stopped to ensure that it did not endanger the unlikely survivor. As onlookers crowded onto the site and gaped, rescuers worked for about an hour before pulling the garment worker free. She was crying, then stopped.

After being given water and biscuits, the woman, who appeared to be about 20 years old, was whisked to Combined Military Hospital in Savar, the suburb of the capital city, Dhaka, where the building collapsed.

There, video showed her lying in bed, a nurse at either side connecting intravenous drips to her arms and a third nurse at the head of her bed. Whenever she raised her head to see what was going on, the nurse in the middle would gently push it back to the pillow and stroke her hair.

"She is fine now," Islam said.

The news spread widely and rapidly; within minutes, Prime Minister Sheikh Hasina had phoned the unlikely survivor and asked about her condition.

"It's an unprecedented incident," she said afterward, according to BSS.

The news agency said Reshma is from northern Bangladesh's Dinajpur district. She has a daughter and was working as a swing operator for Phantom Garment, which had a factory in the Rana Plaza when it collapsed on April 24.

Her rescue, which came on the same day that officials raised the death toll from the collapse by 30 to 1,043, represented a ray of hope against an otherwise grim tableau.

The building had held thousands of people, many of them garment workers.

Though rescue workers had pulled more than 2,400 others to safety, 10 days had elapsed since anyone had been found alive.

Since then, efforts have focused on retrieving corpses from the heap of broken concrete over which bulldozers and cranes have been used to speed the cleanup. Many of the bodies have been so decomposed that authorities have struggled to identify them.

"We are near the end," Islam said.

The owners of the building and the factories are under investigation over accusations they ordered workers to enter the building on the day of the collapse despite cracks that appeared in the structure the day before.

The Bangladeshi government has faced criticism for failing to tighten safety standards in the country's thousands of garment factories, where millions of people work.

The Savar building collapsed five months after a fire at a garment factory near Dhaka killed more than 100 people. And on Wednesday, eight people died in a fire at another factory in the area.

The European Union has threatened to take trade action against Bangladesh if it doesn't improve health and safety conditions for workers.

Western retailers and clothing brands that get their products from Bangladeshi factories are also under pressure to subject their supply chains to greater scrutiny.

The smell of death continues to permeate the area, prompting people passing by on a nearby highway to cover their noses. Recovery workers combing through the debris use face masks to block the stench.

Hundreds of people looking for their missing relatives have been waiting by the nearby school where bodies are taken to be identified.

Authorities have sent some of the remains to a Dhaka hospital for DNA testing, BSS reported. Those that remain unidentified are buried.

Journalist Farid Ahmed reported from Dhaka, and CNN's Tom Watkins reported and wrote from Atlanta. CNN's Joe Sterling, Jethro Mullen and Elizabeth Joseph contributed to this report