Tánaiste Simon Coveney has warned that negotiating a new deal on the future relationship between the EU and UK in less than a year is "ambitious, if not unrealistic".
The UK is scheduled to leave the EU at the end of this month, followed by a 'transition period' until the end of 2020 to allow for trade talks.
British Prime Minister Boris Johnson has set a deadline of December for agreeing on the terms of the future relationship by ruling out an extension to the transition period.
A number of senior EU figures - including European Commission President Ursula von der Leyen and chief negotiator Michel Barnier - have said that not everything will be able to be agreed in that timeframe.
Mr Barnier earlier this week said that they want an "unprecedented" deal that encompasses not just trade, but also other areas such as security, climate action and defence.
However, he warned that more time than 11 months will be needed to reach agreement on every aspect.
Today, Simon Coveney reiterated that the EU wants a "fair and balanced deal" - but told the BBC that they won't be rushed.
Speaking to Andrew Marr, the Tánaiste said: "This is something that Boris Johnson is saying he wants to do in less than 12 months - and I think the European Union has constantly warned that that timeframe is ambitious, if not unrealistic.
"The European Union will approach this on the basis of getting the best deal possible... to ensure that the UK and the EU can interact as friends in the future.
"But the EU will not be rushed on this, just because Britain passes a law."
Mr Coveney also argued that "maybe the penny is finally dropping" for some about the potential consequences to the UK from Brexit.
He observed: "When you leave a union that you've been part of for 45 years, things don't remain the same.
"That is inconvenient, and it has consequences for the UK - the UK has decided to move in a different direction."
On Thursday, British MPs at the House of Commons passed the Brexit Withdrawal Agreement by a significant majority - with the legislation now going to the House of Lords.
The European Parliament must also ratify the deal before the Brexit date later this month.