The Awami League chief spoke about Liton's activities to prevent Jamaat in the northern district at a meeting in the Ganabhaban on Wednesday.
"He (Liton) was always there against the Jamaat. Even Ghulam Azam wanted to hold a meeting there, but he didn't let it happen. He prevented it," the prime minister said.
"Since then, the Jamaat has been irked at him. There were several attempts to kill him. And now they (Jamaat) have finally succeeded," she added.
Ruling Awami League lawmaker Liton was shot by unidentified assailants at his home at Shahbaz in Gaibandha's Sundarganj Upazila last Saturday. He died in the hospital after one and a half hours.
The Awami League leaders have been blaming the Jamaat since the beginning, but the party has denied the allegation, saying the ruling party actually wants to hide the real culprits.
Liton's sisters have urged the law-enforcing agencies to consider all angles in the investigation into the murder.
But Liton's wife Syeda Khurshid Jahan Smrity, a leader of Gaibandha Mohila Awami League, has also pointed the finger at the Jamaat.
She told the media on Tuesday that Liton foiled former Jamaat chief and convicted war criminal Ghulam Azam's rally in Sundarganj in 1998 and the Jamaat murdered her husband to take revenge.
"Jamaat goon Hefza, who had been injured in firing by him (Liton) at the time (of foiling the rally), and many other notorious Jamaat thugs had been threatening to kill Liton through mobile-phone messages and calls," she said.
She vowed to track down the killers of Liton and try them.
This is the first time in a decade that any ruling MP has been murdered. Awami League MPs Ahsanullah Master and former finance minister Shah AMS Kibria were murdered in Gazipur in 2004 and in Habiganj in 2005 respectively.
Several BNP leaders have been convicted for Ahsanullah murder and accused in Kibria murder case.
Hasina said the BNP, a key ally of Jamaat, was doing the 'politics of murder'. "Killing is in the BNP's character," the prime minister said.
She urged the leaders of her Awami League party to be alert over assassination plots.
"I don't know what plans they (BNP and Jamaat) have in mind. They have turned to secret murders after failing to topple the government through movement," she said.
'Character assassination' of Liton
Speaking about the shooting of a boy by Liton, the prime minister said he was a 'victim of character assassination'.
The boy took treatment at Rangpur Medical College Hospital for a long time.
MP Liton had to spend some days in jail in a case started by Sourav's father over the shooting.
Hasina said, "It pains me how the newspapers wrote about the incident and conducted the character assassination of Liton."
"No one revealed the actual incident. Actually he (Liton) was ambushed. The boy was injured in the shooting at that time," the prime minister claimed.
She said the media 'exaggerated' the issue.
"After the case was started, his gun licence was taken back. After the seizure of his gun, he was always in panic of attack. And just that thing has happened now. He has been shot dead at home," the prime minister said.
Addressing the reporters, she said, "Carry out character assassination if you want to, but please don't do something which can cause the loss of life."