Everyone in the UK and Ireland should be afraid of a no-deal Brexit, the Irish taoiseach said, after he was accused of engaging in “Project Fear mark two”.

The taoiseach, Leo Varadkar, was responding to criticism from Arlene Foster, leader of the Democratic Unionist party (DUP), who in turn had been reacting to his comments last week suggesting that the UK crashing out of the EU could increase the chance of Ireland being reunited.

Varadkar said: “In terms of fear, I think we should be afraid of a no-deal Brexit … [it] would have very serious impacts on the economy, north and south, and on Britain. It could have security implications as well and it could have constitutional implications. It’s something that we have to prepare for nonetheless. It is something we should be afraid about.”

His comments came as the British chancellor, Sajid Javid, ordered HM Revenue and Customs (HMRC) to prioritise no-deal planning ahead of the planned exit date from the EU of 31 October.

Javid wrote on Thursday to the outgoing HMRC chief executive, Sir Jonathan Thompson, demanding action to “deliver a functioning regime” on the day the UK left the EU.

In an indication of tensions about HMRC’s attitude towards hard Brexit plans, Treasury sources said Javid’s letter was an instruction to “Whitehall’s unruliest department” to prepare for a no deal. “HMRC must make no-deal preparation their absolute top priority as the UK prepares to exit the European Union on 31 October 2019, with or without a deal,” the chancellor wrote.

Varadkar has been outspoken about the risks he sees as inherent to such plans, leading the DUP, which supports a hard Brexit, to accuse him of not engaging helpfully.

Foster accused Varadkar of behaving “crassly” towards victims of the Northern Ireland conflict in the past after he said moderate unionists and nationalists could question being part of the UK if they were forced into a hard Brexit.

Speaking in Kilkenny on Thursday, Varadkar replied: “In terms of engagement, I have never refused a meeting request from the DUP and never refused a phone call from Arlene either, and she has my number.” He added that he had spoken to the new UK prime minister, Boris Johnson, and had invited him to Dublin to hold further discussions “without any precondition”.

Johnson this week held a private dinner with senior DUP figures as he visited Northern Ireland for the first time since moving into No 10 Downing Street.

Varadkar, asked whether he was worried about Johnson’s ability to be impartial on Northern Ireland, said: “I think that remains to be seen. He’s only just started in the job and I think we need to give him a fair wind and a decent chance.”

He added: “The Good Friday agreement is very explicit that the sovereign government, the UK government, must be rigorously impartial in how it administers Northern Ireland, and we all need to respect the fact that the aspirations about unionist people and nationalist people are equal.”