Police investigating the Grenfell Tower fire say they have carried out 13 interviews under caution.
The Metropolitan Police would not confirm the number of people who had been interviewed but said more interviews were scheduled.
It added more than 7,100 statements had been taken from witnesses, community and family members, emergency services personnel and other sources.
The fire, which destroyed the London block on 14 June 2017, left 72 dead.
Karim Mussilhy, whose uncle was killed in the fire, said the interviews showed "some positive steps" were being taken.
Mr Mussilhy, who is vice-chairman of the campaign group Grenfell United, added that "it would be interesting to find out" who had been interviewed.
Labour MP for Kensington, Emma Dent Coad, said it was "just what our community wanted to hear".
Three interviews had been conducted under caution when police announced a "new phase" of their investigation in July last year.
But they say it could be the end of 2021 before criminal charges are considered.
The Met has said it wants to see the conclusions of the public inquiry's second phase, which starts next year, before compiling a file of evidence for the Crown Prosecution Service to look at.
Phase two will examine causes of the fire, including the use of cladding on the building, which has blamed for helping it to spread.
In 2017, police said they had "reasonable grounds" to suspect that corporate manslaughter offences had been committed.
On Thursday, shadow housing minister Sarah Jones warned that almost 60,000 people were still living in buildings wrapped in aluminium composite material (ACM) cladding - the same type used on Grenfell Tower.
She urged the government to set a deadline for the buildings to be "made safe".
In full: my letter to the Housing Secretary today. Approaching the second anniversary of Grenfell, the risk of another tragedy is still far too high. We urgently need a deadline for tower blocks to be made safe and proper testing on all suspect cladding. pic.twitter.com/vO1CvU8iV2— Sarah Jones MP (@LabourSJ) June 6, 2019
Latest government figures show 166 private residential buildings out of the 176 identified with ACM cladding have yet to have work started to remove and replace it.
The government has promised a £200m fund to help remove the material from private tower blocks.
Ministers have already committed to funding replacement cladding in the social sector, which has 23 blocks still covered with it.
Last month, a government-commissioned independent report into building regulations called for a "radical rethink" of the safety system, but stopped short of recommending an outright ban on inflammable cladding.
The report's author, Dame Judith Hackitt, said indifference and ignorance had led to cost being prioritised over safety and called for regulators to "come together" to ensure building safety.
She also recommended incentives for the right behaviour and tougher penalties for those who breach the rules.
The government has opened a public consultation into improving building safety following the report's publication