"'Daughter of America! We will kill you, just like we killed her,'" she quoted the man on the phone as saying as she stood near the maimed body of Zakia Zaki, the owner of a radio station north of Kabul.
Part of Zaki's face was blown away by three attackers who entered her home and shot her seven times with pistol and automatic rifle fire in front of her 8-year-old son this month.
"'At least people can recognize her from one side of her face. We will shoot your face, and nobody will recognize you,'" Nekzad quoted the caller as saying before she hung up on him.
The lives of Afghan women and girls have improved vastly since the 2001 fall of the Taliban, who stripped women of most rights and made them virtual prisoners in their own houses.
In cities and some rural areas, women can now go to school and work outside the home. But this month has seen a rising number of attempts to quash these advances with threats and violence.
Manizha Naderi, director of the rights group Women for Afghan Women, believes the recent attacks reflect a Taliban resurgence and spike in militant violence across the country. Afghan women in general, and journalists in particular, are being targeted because of their high profiles.
"They want to make news, and targeting the journalists is a way to make news," Naderi said. "They're showing the world, 'We're here and we're still in charge of this country.'"
That is disgusting how these women's violent deaths are being used as symbols. Why are women in particularl being targetted? May I suggest that is it because they have crossed the thin line from being non-existent in public society to taking a visual part of it.
Women have played a large role in the country's media advances the past six years, and several women work on TV news programs as reporters and newscasters. They are typically modestly dressed, with their hair and necklines carefully hidden under scarves.
Still, some Afghans think it is inappropriate for women to appear before the public.
When Afghans talk about Shaima Rezayee, a popular music video show host shot to death in 2005, they speak in hushed tones - about the racy, un-Islamic way she dressed and behaved on TV, as if this justified her death.
And it appears Zaki may have been targeted because of her radio programming.
The radio host had been critical of warlords who warned her to change the programming on her station. Two suspects being held for her slaying are connected with the militant group Hezb-e-Islami, officials said.
In a second killing of a female journalist this month, Shokiba Sanga Amaaj, a newscaster for private Shamshad TV, was shot in her home in Kabul on June 1. Two family friends have been detained in the case.
Authorities say they do not know the motive for the killings of Zaki or Amaaj. Threats in this war-torn and corrupt country are not uncommon.
Nekzad, 29, who works for the news agency Pajhwok Afghan News, forwarded an e-mail to an Associated Press journalist that warned her, "We will kill you as soon as possible, INSHA ALLAH" - if God wills it.
The message, dated June 8, accused her of sexual impropriety and of working for NATO. It was signed "Habib from Hezb-e-Islami," the same militant group authorities suspect in Zaki's death. The authenticity of the e-mail could not be verified.
Nekzad said Afghans began paying attention to her fears only after she told foreign journalists, who took the dangers she faced seriously. She said she wondered if her own role as a journalist could somehow have saved Zaki
Meanwhile, these courageous women are living their lives in fear:
Meanwhile, Nekzad has begun changing her work schedule each day so potential attackers cannot track her routine. She sleeps in a different room of her house every night. She goes without sleep for days, and her speech is punctuated by a cough that she says is caused by stress.
"Maybe they will kill me after six months, after six days, after six minutes," she said. "We know that one day we will leave this world, but if you are informed that you will be killed, it is very, very bad. Every second kills you.