Chief Superintendent Martyn Ripley of British Transport Police said the points could prove "significant".
An eighty-year-old woman was killed and five other people were seriously hurt when the train derailed.
Several carriages were left on their sides after the Virgin London to Glasgow service crashed at Grayrigg, near Kendal, at about 95mph.
Police said 22 people went to hospital after the accident at 2015 GMT on Friday, while dozens more were "walking wounded".
The driver of the train was among those seriously injured.
When the train derailed, a number of carriages slipped down the embankment. One of them came to rest in the air at a sharp angle, while the engine doubled back on the train.
Chief Supt Ripley said he was amazed there had not been more fatalities among the 100 passengers on board. "It is little short of a miracle," he said.
He said his officers were working throughout the train with the Rail Accident Investigation Branch and Her Majesty's Railway Inspectorate.
"Our inquiries have led us to believe that a set of points could be significant in this inquiry, although there is a lot more work to do and we are waiting for further expert opinion," he said.
"We are looking for them to give us an early indication of what caused this accident although it is far too early to tell at this point.
"Our inquiry at the moment is focusing on a set of points."
He also confirmed maintenance had been carried out on the track during the past week, and said most of the passengers had been able to get away from the wreckage unaided.
"When we arrived here a lot of people were in shock. But they were able to get away from the train... the majority were able to walk away," he said.
Police have said the line where the crash happened could be closed for five or six days.
A spokesperson for Virgin Trains said: "The first thoughts of everyone at Virgin Trains are with the families and loved ones of those who have lost their lives or been injured in this terrible accident.
"We will do whatever we can to offer assistance in the days ahead."
Driver locked in cabin
Ian Garnett, watch manager with Cumbria Fire and Rescue Service, was one of the first people on the scene.
He said most of the injured had been in the front two carriages of the nine-carriage train
"The driver was locked inside his cabin for around an hour after we arrived and we had to use cutting equipment to free him," he said.
"He was talking, but he had numerous injuries including head injuries and he also seemed to have a problem with his neck."
Mr Garnett said passengers had been very calm and that a male medical student travelling on the train had helped treat the injured.
Charles Belcher, managing director of Virgin West Coast, said the train's safety record had been closely checked.
"We've examined the safety record of that particular train over the last two weeks to see if there's been any faults, any blips that we can put down to a problem of maintenance and safety, and it got a completely clean bill of health."
One of the passengers, BBC executive Caroline Thomson, said the train "did a sort of bump".
"It suddenly appeared to hit something and then lurched very, very badly from side to side in a very dramatic way."
The 22 passengers needed hospital treatment were taken to three hospitals, with the Royal Lancaster Infirmary and the Royal Preston Hospital admitting the most serious casualties.
A Cumbria Ambulance Service spokeswoman said all but one of the train's carriages had totally come off the tracks.
She added that the wreckage had been cleared of passengers, and that 65 people with minor injuries had been treated at the scene and a nearby farm, before being taken to the Castle Green Hotel in Kendal.
Emergency crews said they had faced difficult conditions, with pouring rain, waterlogged ground and narrow country lanes around the crash site.
The Pendolino tilting trains have been introduced by Virgin over the last three years and have a top speed of 125 mph.
The train rolled down an embankment after derailing
Network Rail said the line speed for the area where the crash took place was about 95 mph.
Virgin Trains have suspended services between Lancaster and Lockerbie, with replacement buses operating. Trains are running as normal to and from Lockerbie, and between London and Lancaster.
A spokesman said passengers travelling between Scotland and London could use GNER East Coast trains instead.
People worried about friends or relatives on the train are asked to ring a Cumbria Police helpline on 0800 056 0146 or a British Transport Police family liaison centre on 0800 40 50 40.
Passengers wanting to travel through Cumbria, meanwhile, can ring National Rail Enquiries on 08457 48 49 50 before starting journeys.
BBCGüncelleme Tarihi: 20 Eylül 2018, 18:16