Coalition MPs have warned the opposition leader, Angus Taylor, not to overreach in talks with Anthony Albanese on Labor’s gambling advertising crackdown, insisting rules that are too stringent would not strike the right balance on personal responsibility.

The prime minister and the opposition leader continued talks on Tuesday over a deal to advance Labor’s legislation to limit online gambling advertising, with betting inducements and more restrictions on advertising hours among possible avenues for movement.

Debate over the issue dominated a meeting of the joint Coalition party room in Canberra on Tuesday, with nine Liberal and Nationals MPs making their views known to colleagues.

Among the contributions were five MPs pushing for tougher restrictions and four arguing the Coalition needed “to get the balance right” and not go too far in limiting advertising. Some warned overly restrictive rules for Australian gambling companies could push some punters to illegal overseas operators, citing comparisons with the rise of illegal tobacco amid rising government excises pushing up retail prices.

Taylor himself raised the question of personal responsibility in a media conference on Monday, an issue that was also raised in Tuesday’s meeting alongside concerns about “over-regulation”.

Coalition MPs used the meeting to raise concerns about “perceived behaviour of gambling preying on the vulnerable”, but the possibility of a deal remained “a moving feast” as parliament resumed after the winter break.

The gambling industry is increasingly resigned to the paring back of inducements, but it says that such restrictions could send gamblers to unregulated offshore operators and particularly impinge the earnings of smaller wagering operators.

Industry sources said they were seeking to warn Coalition MPs about the impact of further changes to inducements or ad rules, but rejected claims from the Greens that they were intimately involved in negotiations.

While Labor sources say they are still confident Taylor will get on board, the Greens are also still talking with the government, signalling a deal with the Coalition is not yet done. Albanese on Monday said publicly he would “later this week” have progress on inducements and advertising rules.

Labor has been criticised for falling short of the ambition of a parliamentary inquiry led by the late Labor MP Peta Murphy three years ago, and is talking with the Coalition and the Greens to find a pathway through the Senate. Murphy’s 2023 committee recommended the government “prohibit all online gambling inducements and inducement advertising, and that it do so without delay”.

Guardian Australia understands some small tweaks to the timing of TV advertising, specifically to lessen the impact on children, could be among the things being considered.

Labor’s proposed changes would see gambling ads restricted to three an hour on broadcast TV between 6am and 8.30pm. But further tweaks to that may be part of the discussions. Other reforms potentially in the frame could be around the discrepancy in ad rules on broadcast TV versus streaming services.

Opt-in provisions for advertising on streaming platforms are also being discussed.

Simon Kennedy, one of the Liberal MPs helping drive tougher action, used a speech in parliament to call for an independent review of the rules after the next election. That plan would help make any newly introduced protections even stronger within three years.

Kennedy said there were “two glaring gaps” in the existing laws: inducements to keep punters gambling longer and unlimited advertising online.

“There should be an independent review of wherever we land after the next election, so we can do more,” Kennedy said.

The government is expected to make amendments to the bill in the lower house, where the bill is listed for debate on Wednesday.