The National Broadcasting Council (KRRiT) said it was examining the allegations.
One came from Culture Minister Marta Cienkowska, who said on Sunday that the channel had aired unverified information, made accusations against the police and carried content that could fuel panic.
"A tragedy is not fuel for political propaganda," she wrote on X.
On Saturday afternoon, a masked 24-year-old drove a car into Kraków’s main square and opened fire on people there.
He was wounded in an exchange of fire with police.
Six people were killed and 16 injured, including two police officers and the gunman, who died in hospital early on Monday.
Council member Tadeusz Kowalski also urged the channel to stop broadcasting content that could encourage behaviour endangering health or safety, saying it breached the broadcasting law.
He pointed to remarks made on air on Saturday by the channel’s editor-in-chief, Tomasz Sakiewicz, who claimed there were no police at the scene because reserves had been sent to Warsaw, to the Constitutional Tribunal.
Kowalski, who described the shooting as a terrorist attack, said police had in fact intervened immediately.
He argued that such claims undermine trust in the authorities and turn a tragedy into a political weapon.
The council said its chair, Agnieszka Glapiak, had launched "explanatory proceedings," a step it takes for every complaint that meets formal requirements.
It will ask the channel for an explanation and a recording of the coverage, then analyse the material under the broadcasting law before making a decision.
The chair has one year from the date of a violation to impose financial penalties.
Broadcasters must keep recordings for 28 days.
(ał)
Source: PAP