(Reuters) - Slovakia's government pushed its controversial overhaul of public broadcaster RTVS through an initial parliamentary vote on Wednesday, just a week after a shooter seriously wounded Prime Minister Robert Fico.

The legislation, which aims to restart the station with a new oversight council and leadership, still must clear debate and a final vote in the coming weeks, but faces little resistance with the government holding a majority in parliament.

The ruling coalition's parties have long been at odds with independent media outlets and have railed against broadcaster RTVS, saying it is not impartial.

The law "aims to ...restore to broadcasting true attributes of public service, balance, independence, objectivity, truthfulness and transparency," Culture Minister Martina Simkovicova told parliament.

Under the legislation, RTVS's director will be replaced years before his term expires, and a nine-member council - appointed by the government and parliament - will be responsible for filling the position.

Opposition parties have raised concerns the law would stifle criticism of the government, curtail freedom of speech and undermine media independence.

"If we approve the RTVS 'cancellation' law, we will get manipulation of public opinion, reduction in freedom of speech, and silencing of voices critical to the government," opposition Progressive Slovakia deputy Rastislav Kratky said before the vote.

The European Broadcasting Union and European Commission Vice-President Vera Jourova have said the overhaul would bring public media under direct government control.

Fico remains in hospital after an attack that officials say was politically motivated, but the leftist-nationalist government has said it would not retreat from its policies.

Since Fico returned to power late last year, his policy shifts, including scrapping the position of special corruption prosecutor, have triggered large public protests.

The government has adjusted its TV overhaul proposal, removing a part that would have installed a programming board, which raised censorship worries, and the possibility that the director could be fired without cause. But criticism has continued.

The Council of Europe's commissioner for human rights, Michael O'Flaherty, wrote on May 7 to Slovak legislators asking them to "give close consideration to concerns that elements of the bill may undermine safeguards for (RTVS's) operational and editorial independence".

(Reporting by Jason Hovet and Jan Lopatka in Prague; Editing by Bernadette Baum)