A spokesman announced private face-to-face talks would now take place between FBU secretary Les Skarratts and deputy fire chief Bill Evans.
He called on the union not to call any further strikes while the talks were ongoing, and said the aim was now to "bring the dispute back into locally and nationally agreed procedures".
Mr Skarratts said: "We're pleased that at least we are now having talks.
"It's a positive development, and we will be going into those talks in good faith."
The fire service spokesman confirmed Acas, the national conciliatory organisation, had also offered its services and was ready to act as a go-between if needed.
He said: "We are prepared to work with them if the FBU are prepared to discuss the financial difficulties of the service, rather than the impossible
demands they are making." The FBU claims plans to cut 120 jobs, 15 emergency fire control operator posts and four fire engines at night-time have left them with no option but to strike.
Firefighters have initially walked out for four days, followed by another four-day stoppage two hours after the first one.
At a meeting on Tuesday, the fire authority agreed to cut 18 more posts at Croxteth Fire Station by merging the fire and rescue teams.
The Daily Post understands around 10 firefighters signed up to work during the strike yesterday walked out to join their colleagues on the picket lines.
But 170 still took up their posts at the 22 of Merseyside's 26 fire stations to remain open during the strike.
Many of them were former firefighters who have since taken on desk jobs and haven't attended fires for years.
Chief Fire Officer Tony McGuirk, Chief Fire Officer for Merseyside Fire and Rescue Service, said: "It's been business as usual for us today, and I think that says a lot about the staff who have shown their commitment to the communities on Merseyside by providing a highly professional service. "We would, however, continue to urge people to take extra care in their homes, at work and when they are on the road."
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