The body of Aram Abdul Razaq Aziz, 32, was found at Watermead Country Park in Leicester on Friday evening.
His former partner Joy Small, 24, who came originally from Sheffield, was found along with their son Aubarr Aziz, three, and daughter Chanarra, two, at a flat in Jersey Road in the city, around two miles from the park.
Leicestershire Police yesterday named the family, while a close friend of Ms Small claimed Aziz was an “abusive monster”.
A police spokesman said: “Officers are investigating the circumstances that led to the deaths of all four.
“No causes of death have been established at present. Post mortem examinations are due to be held tomorrow.
“The deaths of the woman and children are being treated as suspicious. Inquiries are at an early stage, but officers are not looking for anyone else at this time.”
The spokesman confirmed police had previously been involved with the couple but would not give details.
He said discussions had been held with the Independent Police Complaints Commission (IPCC) as to whether the case should be referred to them.
A close friend and neighbour of Ms Small, Jennie Bland, 27, said Ms Small had previously split up from Mr Aziz, then the women fell out when she found out the couple had got back together.
She said Ms Small kept it a secret amid fears her children would be taken from her if anyone knew they were back together.
She said: “She was such a good person, she was a fantastic mum.
“She would have died for those children.”
“We fell out because she got back with him. I couldn’t just sit back and let it happen, I should have just gone on my instincts and told the police and social services.”
Miss Bland described Aziz as an “abusive monster”, adding: “I knew what he was like, I met him a few times, he didn’t like me because Joy could be herself when she was around me.
“She got back with him after being so strong after he poured petrol on her and tried to set her alight.
“He beat her all the time, the time he poured petrol on her he threw a mirror at her son.
“He tried to stop her seeing her friends, that’s why he didn’t like me. He was an abusive monster.”
She said: “She can rest in peace, she is finally away from him and so are the children.”
She said Ms Small, whom she met at their children’s doctors’ surgery in 2008, had ended the relationship and sought help from police, including getting a panic button installed.
But she said she returned from holiday in July to find her friend was different and “more quiet”.
“She said it was because she was with a new boyfriend but I had my suspicions it was him, and they were confirmed in November when we fell out.
“I spoke to her about it and she said she was moving away with him and then yesterday I drove past the flat and saw it was empty so assumed she had moved.”
Floral tributes were placed outside the Jersey Road flat, and a pink and blue teddy bear.
One message read: “To a friend, u’ll be sadly missed so much, sleep tight.”
Others paid tribute to Aubarr and Chanarra, adding: “Taken so soon, sleep tight”.
A neighbour who lives opposite the flat, who did not wish to be named, said she only knew the couple to say hello.
“She was a lovely woman, really nice,” she said.
“They lived here together and then he moved out. I can’t believe it, I’m really shocked.
“I just came home at 3pm and everything was here, about five police cars, an ambulance and paramedic and then a private ambulance.
“My first thought was, ‘What’s Aram done, has he hurt the kids or Joy’, I didn’t think it would be all of them.”