Water flowing into Toddbrook Reservoir was "reduced considerably" overnight but engineers remain "very concerned" about the integrity of the damaged 180-year-old structure, which contains around 1.3 million tonnes of water.
Hundreds of people have been evacuated from the Derbyshire town of Whaley Bridge over fears it could rupture and flood their homes.
South Yorkshire Fire and Rescue is assisting colleagues in Derbyshire by providing a high-volume pump from Aston Park fire station in Sheffield to help lower the water level so workers can make the dam safe.
Meanwhile, the Sheffield to Manchester Piccadilly rail line through the Hope Valley is blocked and expected to be closed until next Tuesday morning.
Julie Sharman, chief operating officer of the Canal and River Trust which runs the reservoir, said water levels had reduced by around 8in (200mm) overnight.
She said: "It is a critical situation at this point in time. And until we're beyond that critical situation, the risk is a material risk and that's why we've taken the action we have."
Ms Sharman said engineers have told her the crucial puddle clay core of the dam is intact, but it is vital to replace the load on the core lost when the earth was eroded.
An RAF Chinook and firefighters using high-volume pumps appear to have partly stabilised the "unprecedented, fast-moving, emergency situation" caused by heavy rain.
The Chinook has been dropping one-ton sandbags on to the damaged area to bolster the structure.
Improving weather and work on the inflows means the amount of water entering the reservoir has also reduced.
Derbyshire Chief Fire Officer Terry McDermott said there are 150 firefighters working at the reservoir with 10 high-volume pumping crews.
But he said despite progress, engineers remain "very concerned" about the situation.
Mr McDermott said: "The structural engineer is saying if we don't do something there will be a problem.
"It's not going to go away on its own. It's absolutely necessary, the activity that's going on at the moment."
The 10 pumps are currently being used to get around 4.2 million litres of water an hour out of the reservoir, the National Fire Chiefs Council said
They are expected to continue shifting water for around two to three days, it added.
Police have also closed railway lines in the Whaley Bridge area over the risk of potential flooding.
Prime Minister Boris Johnson said "first responders, engineers and RAF crews are working around the clock to fix the dam" and he has ordered Environment Secretary Theresa Villiers to chair a meeting of the Cobra emergency committee to discuss the situation.
Around 1,000 people were evacuated from the town but most found their own accommodation with family and friends, according to Derbyshire County Council.
Julie Odams, the authority's assistant director of communications and customers, said: "The evacuation generally was very, very smooth but it was disruptive for people and the time for leaving wasn't great so people weren't able to collect everything they wanted to.
"We've not had anybody who's been very distressed or anything like that."
Police said a timescale for the evacuees to return home is "currently unknown".
Carolyn Whittle, who lives in Meadowfield on the hillside in Whaley Bridge, said: "I've lived in Whaley for the best part of 45 years and I've never seen water flood over the dam like that, ever, nor thought that we could possibly be at risk in this way."