Investigators have said they are following a number of leads and released photos of a four-door, dark-grey Volkswagen sedan.
It was left unclear how the car was tied to the case, and police said they had yet to determine whether they were seeking one or more suspects. Several law-enforcement agencies — including the FBI — are now involved in the investigation.
The authorities have described the killings as "ambush shootings", which were carried out near a mosque and a charity centre that helps refugees. On Sunday they said the attacks could be linked, given the similar methods used.
Ahmad Assed, the president of the Islamic Centre of New Mexico, said the city's Muslim community was going through "a sort of managed panic".
The killings have shocked the community and prompted statements against hate crime from US President Joe Biden and Vice President Kamala Harris.
The most recent victim was killed on Friday evening after attending the funerals of two other victims.
Muhammed Afzaal Hussain, 27, a planning director for the city of Espanola who immigrated from Pakistan, was shot dead on August 1 outside his apartment complex.
This was less than a week after Aftab Hussein, 41, from Albuquerque's large Afghan community, was found dead on July 26 near the city's international district, police said.
Hussain had also worked on the campaign team for Melanie Stansbury, a member of the US House of Representatives.
Police said they were treating those two murders, along with Friday's killing, as being linked to the November 7 murder of another Afghan Muslim, Mohammad Ahmadi, 62, who was shot dead in a car park outside a halal supermarket.
Security stepped up
Albuquerque Mayor Tim Keller said the state authorities were working to provide an "extra police presence at mosques during times of prayer", as the investigation proceeds in New Mexico's largest city, which is home to as many as 5,000 Muslims out of 565,000 residents.
New Mexico Governor Michelle Lujan Grisham has described the shootings as "targeted killings of Muslim residents".
Mr Biden posted a message on Twitter on Sunday expressing solidarity with the Muslim community, adding: "These hateful attacks have no place in America."
The three latest victims belonged to the same mosque, according to Tahir Gauba, another Islamic Centre of New Mexico representative. Officials were withholding the identity of the man killed on Friday pending notification of next of kin.
But Mr Gauba said the man was killed shortly after attending the funeral for the two previous victims.
"There are several things in common with all four of the homicides," city police spokesman Gilbert Gallegos said on Sunday.
Asked whether investigators consider the killings to be hate crimes, Mr Gallegos said: "Hate is determined by motive, and we don't know that motive at this point."