Those accused have denied the allegations, the newspaper said.
Awami League activists have been accused of violence in their efforts to regain political hold on the party's returning to power.
Hasina has time and again issued warnings to her partymen. Some weeks ago, she resigned from the youth and students bodies of which she was the symbolic chief when they engaged in factional wars.
The leaders sat on hunger strike to protest her action.
The Daily Star said in an editorial Thursday: 'We fully share her views on the issue of MPs exerting influence on the bureaucracy to extract undue advantages for the ruling party activists.'
The editorial deprecated the 'argument' from some AL quarters that they were doing precisely what the rival Bangladesh Nationalist Party (BNP) and its allies had done when they were in power.
Urging AL leadership to 'go beyond condemning' acts of highhandedness, the editorial suggested: 'The ruling party should have its own version of intelligence that will let the leaders know where things are crossing the limits of acceptability and who are responsible for it.'