Tánaiste Simon Coveney has said the Republic would back an extension to Article 50 if the British prime minister can make a persuasive case for how it can be used to get a Brexit deal.
Mr Coveney said the Republic would support a request from the British government to extend the Brexit deadline, currently October 31, if it "made sense".
Speaking at an event to get Irish businesses ready for Brexit, Mr Coveney said: "If there is an extension looked for then I think whichever prime minister asks for that will need to make a persuasive case as to how that extension can be used to get a deal.
"Ireland's position has always been if it makes sense to extend to try to get a deal, well then we would support that course of action.
"What we need to do is control what we understand, and what we control here in Ireland, and that is preparing for the worst but continuing to think about how we can work with a British government regardless of who leads it between now and the end of October."
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Mr Coveney said the EU cannot do a deal with Mr Johnson's government unless it puts forward Brexit backstop alternatives.
He said: "We have a deal as far as we're concerned, it's called the Withdrawal Agreement, and we spent two and a half years negotiating it.
"It solves some very complex problems on this island that aren't just about trade. They're also about identity, about peace and about relationships.
"The backstop gives reassurance, albeit on a temporary basis, on those issues because it provides guarantees.
"If you are advocating, as Boris Johnson has done, that we need to remove the backstop from the Withdrawal Agreement, well then the obligation is on you to make a convincing case that you have an alternative that does the same job.
"Otherwise, you expose a whole series of problems without answers and that's why we've said that this process can't make any progress unless and until the British government comes forward with actual proposals that make sense so that we can interrogate them."
His comments come as the Dublin government launched a national campaign urging businesses to review how prepared they are for the UK leaving the EU.
The British government has warned businesses that the risk of a no-deal exit is growing,
Sectors which they said have low levels of Brexit preparedness include smaller businesses that may not realise they are trading with the UK, construction businesses, manufacturing companies, agrifood businesses, retail - particularly independent shops - and hauliers.
The British government appealed for businesses to understand the new rules for UK importing and exporting, to review their supply chain and UK market strategy and be aware of any changes to transport and logistics.
Firms have also been asked to review their certification, regulation and licensing, contracts and data management and ensure businesses are maximising government Brexit programmes and supports.
"Manage your cash flow, currency and make sure your banking is in order, protect and inform your staff and know more about the impact to your sector," businesses were told at the event in Dublin.
