The UK's stance on the customs backstop is no cause for panic, the taoiseach (Irish prime minister) Leo Varadkar has said.
Monday's vote in the House of Commons ensured there would be no customs border down the Irish Sea.
It effectively rendered the EU's backstop vision unlawful.
The DUP supported the Commons move on a customs border, but the SDLP and Alliance fear the prospect of a no deal scenario.
The Irish government's position is that there can be no Brexit deal without a backstop to prevent a hard border on the island of Ireland.
Mr Varadkar said a deal was still possible but added his government will "step up our preparations for a no-deal scenario".
'Twists and turns ahead'
Although he described that outcome as unlikely, he said preparations were necessary because "we can't make assumptions that the Withdrawal Agreement will get through Westminster".
"It's not evident, or not obvious, that the government of Britain has the majority for any form of Brexit quite frankly," the taoiseach told Irish broadcaster, RTÉ.
He added there was "lot of political instability in London and turmoil in Westminster, and we're going to see a lot more twists and turns in the months ahead".
But Mr Varadkar said the vote by British MPs should not result in any change to the Irish government's position.
Earlier, a spokesperson for the Irish Department of Foreign Affairs said: "It is fully accepted and understood that there can be no Withdrawal Agreement without a legally operable backstop ensuring that there will be no hard border."
The EU's proposal on the backstop would have kept Northern Ireland in the customs union and the single market for goods.
But Monday's amendment to the Customs Bill would make it illegal for Northern Ireland to be outside the UK's customs territory.
The Irish Department of Foreign Affairs said it had been the UK government's position that customs checks between Northern Ireland the rest of the UK are unacceptable, so it was not surprising that the amendment to the Customs Bill was accepted.
It said the UK has also "repeatedly committed to avoiding a hard border [on] the island of Ireland, most recently in last week's White Paper".
"In fact, the Withdrawal Act, passed last month, legally binds the UK government to this commitment," it added.
It said the Irish government had always been clear that its "first preference, in terms of avoiding a hard border, is through the closest possible future EU-UK relationship".
"It is not for the Irish government to comment on the internal politics and legislative processes of the UK… what matters is that the British government is able to engage in serious negotiations with the commission."
Sinn Féin's Deputy Leader Michelle O'Neill has accused the UK government of "duplicity" and called on the Irish government to seek "cast-iron legal guarantees" to protect the backstop.
"What Theresa May did last night was effectively tear up her own proposals from Chequers. Her government is in chaos and in her rush to placate the DUP and the Brexiteers, she has now made a 'no deal' crash scenario much more likely," Mrs O'Neill said.
"A crash will have a devastating impact on the island of Ireland so there is now an increased onus on the Irish government and our EU partners to ensure our national interests are protected in the ongoing Brexit negotiations."
The leader of Ireland's biggest opposition party, Fianna Fáil, has expressed his concern about the implications of the latest Brexit votes in the Commons.
Micheál Martin said Mrs May had lost room to manoeuvre in negotiations with the EU.
He said that if the SDLP still had representatives in Westminster they would have worked to defeat the votes, referring to Sinn Féin's abstentionist stance.
"What happened... was not constructive and is damaging to the entire island of Ireland," he said.
"It is the once in a generation issue that trumps every other issue, I think that the abstentionist position of Sinn Féin is not helping the overall Irish cause," he added.
Earlier, SDLP leader Colum Eastwood accused Prime Minister Theresa May of "cowardice" and caving into the demands of hard-line Brexiteers.
It followed the government decision on Monday to agree to a legal guarantee that there will be no post-Brexit customs border in the Irish Sea.
The SDLP and Alliance said there is now a real danger of the UK crashing out of the EU with no deal.
However, the Democratic Unionist Party (DUP) said the move would preserve peace.
The proposers of "New Clause 37" - an amendment to the Customs Bill - argued that it would prevent a border between Northern Ireland and the rest of the UK.
On Monday night, MPs approved the clause without going to a vote, but two other amendments tabled by Tory Brexiteers scraped through by just three votes in the Commons.
New Clause 37 directly contradicts the EU's legal draft of the so-called "Irish backstop", which suggested Northern Ireland should be treated as part of the European Union's customs territory.
That legal version of the backstop has already been rejected by Mrs May. However, the prime minister has said she will abide by the principles of a protocol on a future backstop which it negotiated with Brussels in December.
The amendment was backed by both the DUP and the pro-Brexit Conservative European Research Group or ERG.
The UK is due to leave the EU on 29 March 2019 and Parliament is considering a number of new laws needed to prepare for this and for life after the end of a proposed transition period.
Meanwhile, the government has survived a challenge to a key element of its Brexit policy by just six votes.
An amendment to the Trade Bill which would have committed the government to staying in a customs union if it cannot negotiate a free trade for goods was rejected in the House of Commons by 307 votes to 301 on Tuesday.