The call from Washington came around 9pm on Thursday, her Press Secretary Ihsanul Karim said.
Secretary Kerry spoke for nearly 16 minutes and expressed concern over the murder of Xulhaz, a former staffer at the US embassy in Dhaka, and his theatre activist friend Mahbub Rabbi Tonoy.
Calling Xulhaz ‘our colleague’, Kerry asked the prime minister to bring the killers to justice, Karim said.
Armed assailants barged into the Kalabagan residence of Xulhaz on Monday and hacked him to death along with his friend Tonoy.
The attack had striking similarities to some of last year's murders of secular bloggers and liberal thinkers.
Although the al-Qaeda in the Indian Subcontinent has purportedly taken responsibility for the murders, the government doubts the credibility of the claims.
The US has offered help in the investigation.
Karim quoted Hasina as telling Kerry, “Our position is firm against terrorism. We are following a ‘zero tolerance’ policy. Our law-enforcing agencies are working hard.”
“Some clues have been found. We hope we will be able to spot and bring the killers to book,” she added.
The prime minister reminded Kerry that Xulhaz was a cousin of Awami League leader and former foreign minister Dipu Moni.
Reminding Kerry that most of her family members had fallen to assassin’s bullet, Hasina said Thursday was the birthday of Sheikh Jamal, her brother who along with the rest of the family was murdered on Aug 15, 1975.
She said two of the killers of her family were in the United States and requested that the US return them, Karim said.
Hasina hoped the cooperation between Dhaka and Washington to tackle terrorism would continue and the US would provide information if it gets any.
According to Karim, Kerry told Hasina that the US would send Nisha Desai Biswal, Assistant Secretary of State for South and Central Asian Affairs, to Bangladesh to take the cooperation related to counter-terrorism forward.
The prime minister said she believed “those who burnt people alive openly in 2015 are backing the current murders”.
“The killers have taken a soft-target policy in the killings. They are targeting imams, priests. These are cold-blooded murders,” Karim quoted her as telling the top American diplomat.
The prime minister also expressed concern at the recent murder of eight people of a family in the US as well as the murder of the Bangladeshi couple in San Jose, California.