He told ournalists, Censor.NET reports citing Ukrainski Novyny.
Lutsenko called Parasiuk's attack on journalist Andrii Dzyndzia and National Guard fighters unacceptable.
"Today, Interior Ministry investigators who launched relevant proceedings and carried out relevant investigative actions are meeting with prosecutors. If there are enough grounds, the case will be referred to the Main Investigation Department of the Prosecutor General's Office, which may lead to an indictment against Parasiuk," Lutsenko said.
He also admitted the probability of stripping Parasiuk of immunity.
Previously, the police launched a probe into the conflict at a checkpoint in Sloviansk with the participation of Verkhovna Rada MP Parasiuk.
Seven policemen were injured as a result of the clash.
Related materials: Blockade of "DPR/LPR"
Shock, not disaster, - German experts estimated losses to Ukraine’s economy caused by Donbas blockade(0)
PM Hroisman: Ukraine to purchase coal from US, Australia or South Africa, pay foreign currency for it(0)