Simon Coveney says the EU won't allow a situation 'where everything else is concluded except the border issue'
The Tánaiste has insisted 'substantial progress' has to be made on the Irish border issue before the next major Brexit deadline in June.
EU leaders will meet in June, and that summit is seen as one of the key deadlines ahead of Britain leaving the EU next year.
There is an ultimate deadline of October for the overall withdrawal treaty to be agreed, so it can become law before the full withdrawal in March 2019.
The Taoiseach has previously indicated he would rather the right deal on the Irish issue in October rather than 'any deal' in the summer.
Speaking on Newstalk's On The Record, Simon Coveney observed: "What the Taoiseach said was that he'd rather get the right deal in October than an early deal that wasn't the right deal in June.
"We don't [have until October]. We need to see substantial progress in June, to reassure people that we're moving in the right direction for October.
"What we won't allow is to allow these negotiations to get to October, and to have everything else concluded except the Irish border issue because it's politically difficult."
The Tánaiste argued that while some British cabinet ministers - including Brexit secretary David Davis - have appeared to downplay the 'guarantees' that have been agreed on the subject of the Irish border, it is the prime minister's actions that count.
Minister Coveney explained: "People in Westminster have been saying various different things, but the British government position - signed up to by the British prime minister - in December was very clear: that they will provide guarantees is the word of no border infrastructure, and no related checks and controls.
"I think we need to take our lead from the Brexit negotiations from the prime minister [...] David Davis has said various things... a lot of positive things too more recently in relation to the border, because he visited the border."
The Tánaiste also pointed to the 'backstop' agreement, which pledges that a “common regulatory area” will be established in Northern Ireland following Brexit if no other solutions to the border issue can be found.