A plan to ban ads for online gambling within three years has already come under fire, with the crossbench urging the government to act sooner, and television and gambling industries raising the possibility of compensation or a watering down of the proposed ban.

On Wednesday a parliamentary inquiry called for the phased introduction of a comprehensive ban on the ads, moving through the opposition’s preferred model for a ban during game time and an hour either side, towards a ban between 6am and 10pm, and finally a total ban.

Although the report was unanimous, the government faced calls to go further from the Greens and independents, including Zoe Daniel, Andrew Wilkie and Rebekha Sharkie, who proposed a 12-month phase-in period.

After Labor committed only to consider the recommendations, Greens senator Sarah Hanson-Young said she was “concerned that the government has not backed them immediately”.

“Gambling ads should be banned by footy finals time,” she said. “Three years is too long … [It] means three more years of gambling ads fuelling addiction, wrecking lives and affecting children.”

Daniel said the timeframe would “enable the gambling giants and other vested interests to lobby to water down the recommendations and dilute the government’s resolve to act”.

“Given the committee has acknowledged the extent of the problem, the government should act now and ban all gambling advertising wherever it appears as soon as legislatively possible,” she said.

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Free TV Australia, which warned the inquiry that free sports broadcasts could be cut as a result of a ban, warned against what it called a “kneejerk” response that “will ultimately hurt viewers and the television services they love”, according to the chief executive, Bridget Fair.

“Measures like frequency caps would be a better and more targeted approach to respond to any community concern around volume of advertising,” she said.

“Any further restrictions on gambling advertising must be offset by reductions in the regulatory burdens on commercial broadcasters.

“In particular, removing spectrum fees, which are completely out of step with other countries that have already abolished such fees decades ago.”

The Responsible Wagering Australia chief executive, Kai Cantwell, claimed the ad ban was “shortsighted [and] ineffective” because Australians would turn to “illegal offshore markets”.

It also backed a cap rather than a ban on ads, arguing this would meet community expectations “while also maintaining the crucial support to sporting codes and local broadcasters”.

Sportsbet, one of the largest wagering services providers, supported recommendations including banning commissions and ensuring the use of data-led intervention, but warned the ad ban was disproportionate.

The Sportsbet chief executive, Barni Evans, said “significantly” reducing ads would “respond to community concerns, while still supporting sport and media”.

“It is important that any changes in regulation recognise that gambling is a lawful form of entertainment enjoyed responsibly by millions of Australians.”

The chair of the House of Representatives standing committee on social policy and legal affairs, Labor MP Peta Murphy, said the inquiry recommended a phased approach because it recognised “that broadcasters, sporting organisations and advertising companies are currently quite reliant … on revenue from gambling companies”.

“We didn’t want a kneejerk reaction to say that everything must change tomorrow – but everything must change and we tried to lay out a roadmap for a government about how you might get there,” Murphy told the Guardian’s Australian Politics podcast.

Murphy said it was “not a bad thing” that “both extreme sides” of the argument thought the committee had gone too far or not far enough.

Murphy noted the report allowed there “may well be exceptional circumstances, which may mean it may need the final phase to be longer than three years, which would be for example for contracts that absolutely couldn’t be broken”.

“We’ve tried to be reasonable and measured about it but say this is not an opportunity to kick it off into the long grass.”

Before the release of the report, the prime minister, Anthony Albanese, labelled gambling ads “annoying” while the communications minister, Michelle Rowland, agreed that the “status quo isn’t good enough”.

On Wednesday Rowland and the social services minister, Amanda Rishworth, said they would consider the inquiry’s recommendations.

The opposition leader, Peter Dutton, said he would wait to see the response from the government, but noted in his budget reply he had stated “that gambling ads have gone way too far”.

Mark Kempster, a recovering gambling addict who told the inquiry he received sports gambling advertisements despite requesting a lifetime ban from betting, said gambling companies had “acted with such little duty of care for so long to the harm they have caused in society”.

“I am really pleased to see the recommendation regarding a levy being placed on all gambling companies to pay for a national strategy into harm deduction.”