Prime Minister Theresa May is struggling to find ways to get MPs to back her unpopular accord, but her junior Brexit minister Martin Callanan said the government would not postpone Britain's departure beyond the scheduled date of March 29.
But there has been talk for several weeks that British and EU officials are quietly exploring the possibility of extending Article 50 -- the legal process for the UK leaving the bloc -- to give May some breathing space.
Another junior minister added fuel to the fire on Monday when she said the government may have to delay Brexit if it loses a crucial vote on May's deal next week.
But as he arrived for a meeting with fellow EU ministers in Brussels, Callanan insisted the government was not changing course.
"We're very clear -- the policy of the government is that Article 50 will not be extended," Callanan said.
"We are leaving the EU on the 29th March this year, because that's what Article 50 says, that's what parliament voted for and that's now what domestic British legislation says."
She postponed the vote last month because of intense opposition from MPs, promising further clarifications from the EU, but talks with numerous European leaders in recent days have not yielded a breakthrough.
The EU insists the deal, which took two years to negotiate, is now closed and substantive talks cannot be restarted.
"I don't work on hypotheses -- the current situation is complex enough... Let's stick to here we are now," she added.
Sources have told AFP for several weeks that Britain has been discussing the possibility of delaying Article 50 with European officials as a possible fallback scenario.
An EU diplomat told AFP "it is clear that everyone has in mind that this possibility exists", but cautioned that "it is a very hypothetical option and not the privileged scenario of anyone".
Any extension to Britain's departure would be complicated by the elections to the European Parliament in May. The EU diplomat said this meant that an extension would be "narrowly limited to weeks or a few months" -- perhaps no later than the end of June or early July.
As she tries to persuade her MPs, May has promised she will seek "political and legal reassurances" from the EU over the use of a temporary arrangement designed to keep the border with Ireland open after Brexit.
Many from May's Conservative Party, and Northern Ireland's tiny Democratic Unionist Party (DUP), which props up her government, fear the so-called backstop will keep Britain indefinitely tied to the EU's single market rules.