The Tanáiste has told the Dáil that in a no-deal Brexit scenario it would be impossible to maintain "the current seamless arrangements between the EU and UK across the range of sectors" .
Mr Coveney was speaking as the Dáil prepared to debate the Omnibus Bill which seeks to prepare the country for a no-deal Brexit.
Mr Coveney also told the Dáil that "however much we wish, we're not going to wake up to find the last two and a half years have been a dream".
"The UK is leaving the European Union and today we still don't know how or under what conditions".
The Bill contains 15 parts, addressing primary legislative issues which require immediate attention in a no-deal scenario. Other issues will be addressed by Statutory Instruments.
Mr Coveney said that in the event of the Withdrawal Agreement being ratified, the Bill would make provision in domestic law for a transition period during which EU rules and regulations will continue to apply to the UK, even though it be formally a third country.
Among the provisions in the Bill is the protection and provision of the Common Travel Area between the Republic of Ireland and the UK.
The Bill also provides for continuity for a range of existing healthcare arrangements between Ireland and the UK, the continued payment of a range of social protection benefits such as old age pensions, and the continued mobility of higher level students.
Mr Coveney said the Bill addresses sectors where major challenges associated with a no-deal Brexit had been identified, including all island transport and energy.
It will protect cross border bus services, and covers compatibility with EU rules on areas such as recognition of driver qualifications.
It also enables the Energy Regulator to maintain the operation of the Single Electricity Market in the event of a no-deal Brexit.
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On supports to businesses, Mr Coveney said the Bill would introduce postponed accounting for VAT purposes, to alleviate the impact of potential cash-flow difficulties in a no-deal scenario.
On the time-frame for the bill, the Tanáiste said it is intended it will complete Committee and Report Stage of the Dáil next week and go the Seanad for debate between the 11-14 March.
Mr Coveney said this would see the bill enacted in time for 29 March, although he acknowledged that the "timelines are tight".
Fianna Fail's Brexit spokesperson Lisa Chambers said her party is 'disappointed' that this Brexit Omnibus Bill was only published last Friday, adding that the Opposition had been given 'insufficient' time to properly scrutinise the Bill.
Ms Chambers also said the Bill did not address the border issue in a no deal scenario and there was no clarity on how the Government intends to protect the single market and the Union's Customs Code in the event of a no-deal Brexit.
Sinn Féin's Brexit spokesperson David Cullinane labelled the Omnibus Bill as "the bare minimum needed in terms of Brexit planning".
He said his party would not be seeking to delay the legislation but would not be giving the Government "a blank cheque".
Mr Cullinane added that Brexit will mean a structural change to the Irish economy and would be "one of the biggest market distortions to impact on Irish businesses" and called for State intervention, State supports and investment.
He welcomed the provisions of the Bill and said his party acknowledged that we need to plan for a no deal scenario. He stressed the need for avoiding any hardening of the Border.
People Before Profit-Solidarity TD Richard Boyd Barrett said while he welcomed the practical measures in the Bill to maintain the status quo in key areas, the legislation did not address the threat of a hard border.
"We still do not know from the government what it is going to do in the event of a no deal, where pressure comes from either the UK or the EU to impose a hard border," Mr Boyd Barrett warned.
He warned a hard border would "be a total disaster" and would "drag us back to the dark days of conflict and division".
Mr Boyd Barrett said the bill should include a statement that a hard border would not happen. 1849
He also called for investment in public enterprise to mitigate any job losses.