The government is considering restoring the pandemic unemployment payment to its previous amount, according to Thomas Byrne.
More than 100,000 more people are expected to lose their jobs when the country moves to a mix of level four and level 5, with the closure of non-essential retail expected to be announced later on today.
Many have flagged that social supports, as well as a blanket ban on evictions, must be brought back in, in order to protect people.
"That's a key issue that's under consideration this weekend by the government," the Minister of State for European Affairs said on RTÉ's.
"Social solidarity; we won't have that unless we have the supports in place, and they are exactly the considerations that government is considering, before a final decision is made, to make sure that we protect the health of the population, but also protect the country as economically as we can."
Evictions are supposed to be banned until January next year, but more than 300 people have been evicted during the pandemic so far.
Mr Byrne said the government will implement further restrictions to deal with the issue.
Mr Byrne said he "would expect that the restrictions will be brought even tighter and much stronger".
"We're going to make sure that they don't happen. They shouldn't have happened with a ban there.
Schools are to remain open in any new restrictions however the government are currently examining rolling out rapid antigen testing, similar to that in France, across schools.
Sinn Féin president Mary Lou McDonald's said a "weekend of speculation" has been worrying and additional restrictions "have to be matched by additional support".
"Our strong view is that, respecting the fact that people are going to struggle with new restrictions and offering the support that the state can financially and in terms of the security of the roof over their heads, is a very direct way to help that sense of social cohesion and to rekindle perhaps that have often used phrase that we are all in this together."
Ms McDonald also said she felt a six-week lockdown would be "really, really challenging and difficult for all of us".
"I also know that last week in 13 hospitals public hospitals across the stat there was no intensive care capacity," she said.
"People who are going to really struggle and who are as we're speaking this morning, many of them, worried sick, it's imperative that the state acts to restore the PUP and the wage subsidies by the way, and reinstate an absolute ban on evictions."