Ian Reid and John Averis were based in Stratford
Fire crews will not stop their search of a warehouse devastated by fire until the bodies of their missing colleagues are found, a spokesman has said.
Crews are carrying out an inch by inch search of the vegetable plant in Atherstone on Stour, Warwickshire which set alight on Friday evening.
One firefighter has been confirmed dead and three are still missing.
The county fire service chaplain named the men as Darren Yates-Badley, Ashley Stephens, Ian Reid and John Averis.
Four football pitches
Jon Hall, assistant chief of Hereford and Worcester fire service, which is carrying out the search, said it had been an extremely frustrating day as crews had to search an area the size of four football pitches.
He added he hoped the area would have been cleared by midnight on Monday but it was now clear this would not be the case.
Ashley Stevens and Darren Yates-Badley were based at Alcester
"But due to the state of the building and the conditions crews are having to work in we can no longer say how much longer this operation will take.
"We will not stop operations until we retrieve the Warwickshire firefighters who are still in the building," he said.
Earlier, he said the 150 staff who worked at the site had all been accounted for.
When the bodies are found, members of Warwickshire Fire and Rescue will carry them out of the building, as a mark of respect, the service has said.
Warwickshire Police said on Monday they had not yet established the cause of the fire which "remains suspicious".
One of the four firefighters was confirmed dead after being pulled from the fire.
Ian Reid, 44, had worked for Warwickshire Fire Service for four years, being based in Rugby and Stratford.
Three of his colleagues were still in the burning premises when the roof collapsed.
Darren Yates-Badley, 24, was based at Alcester and leaves behind a wife, Faye and parents Mandy and Stephen.
Ashley Stephens, 20, was also based at Alcester. He leaves behind a fiancee, Emma Crocker, with whom he had a three-month old son, George.
And John Averis, 27, was based at Stratford. He had been with Warwickshire for three years, previously working as a Ministry of Defence firefighter at Marlborough Barracks.
The search operation, involving more than 100 fire officers from Warwickshire, Hereford and Worcester and the West Midlands, began on Sunday.
Canon David Capron, the county fire service chaplain, praised the men's "loyalty and heroism" at a service in Alcester on Sunday.