David Davis has signalled that discussions on the UK's exit from the European Union (EU) may not start on June 19 as anticipated.
The Brexit Secretary said the talks would take place that week, but not necessarily on the Monday due to the clash with the Queen's Speech at Westminster.
Mr Davis also indicated "we will start down this process" by focusing on the divorce proceedings from the EU before moving on to trade.
Brussels has insisted that talks on the so-called divorce, taking in issues including the fee the UK will have to pay to sever its ties, must make sufficient progress before any discussion on a future trade agreement could begin.
The UK Government wants the talks to take place in parallel during the Brexit process.
Theresa May had repeatedly said during the election campaign that the Brexit talks would start 11 days after the June 8 vote, using it as a warning that Jeremy Corbyn's Labour were not ready for the negotiations.
Mr Davis indicated there could be a slight delay before he enters the negotiating chamber.
He told Sky News: "It's in the week of next week, basically, the first discussions.
"My permanent secretary is actually in Brussels today talking to them about the details.
"It may not be on the Monday because we also have got the Queen's Speech that week and I will have to speak in that, and so on. "
Mr Davis added: "In the first round we are going to have pretty long meetings at roughly one week a month - which is much, much faster than any previous trade deal they have done.
"The first bit of it - Brussels want to do the so-called divorce proceedings first - the first bit of that includes European citizens in the UK.
"It includes money, they want to talk about that, we think it should come later, and Northern Ireland.
"The European citizens in the UK, we want to get on with as fast as possible because we don't want people to be in a state of anxiety."
Dismissing the prospect of a unilateral decision to guarantee the rights of EU citizens in the UK, he stressed he had "got to worry about the million or so Brits abroad".
Asked if he was now accepting Brussels' timetable, as set out by chief negotiator Michel Barnier, Mr Davis said: "What we have said is we will start down this process but I will have some discussions with Mr Barnier about how we progress to the wider thing of the trade area.
"The most important thing in the aggregate is the trade area."
Mrs May's weakened position in the House of Commons as a result of losing her majority has fuelled speculation the Tories would be forced to soften their stance on Brexit.
Mr Davis suggested he was open to co-operation with Labour on the issue but rejected the idea of the UK remaining in the single market.
The EU had made clear "you cannot stay in the single market and have control of your borders" and "there's no sign of them changing their position".
He added that Labour's position in its manifesto was "very similar to ours" and added, if shadow Brexit secretary Sir Keir Starmer "or frankly anybody in the House of Commons" had ideas on how to handle the talks, he would "take it on board".
"But it's got to work, that's the point," he said.
"This is not a piece of political gamesmanship, it's got to work, it's got to actually deliver on what the people asked for which is control of the borders, control of laws, control of money and it's got to deliver a decent economic outcome and protect security."
Senior Tories including Ruth Davidson and Chancellor Philip Hammond have stressed the need to put the economy first in the negotiations, which has been taken to suggest disagreement with the focus on curbing immigration.
Shadow international trade secretary Barry Gardiner also appeared to soften Labour's stance on membership of the single market, acknowledging it was "an open question" whether Britain could remain inside the arrangement which would require maintaining freedom of movement.
But shadow foreign secretary Emily Thornberry said it was "difficult to envisage" how that could happen.
Shadow chancellor John McDonnell and Labour leader Jeremy Corbyn have previously said Britain would have to leave the single market after Brexit.
Mr Gardiner told BBC Radio 4's Today programme: "It's an open question as to what we can get.
"What we criticised her (Theresa May) for doing was taking membership of the single market off the table right from the beginning.
"It's quite ironic because she was the one who said that you had to take certain things off the table, and she said that we should not take off the table a no-deal outcome, which of course seemed crazy to most people.
"But she has taken off the table membership of the single market.
"We've said let's look at that and see if it can be reformed.
"But the key thing is not to get hung up on the membership of the single market, but to be assured of the benefits that it can bring for our economy and for our jobs."
Ms Thornberry told BBC2's Victoria Derbyshire programme: "We are leaving the EU.
"We find it very difficult to envisage how we could remain in the single market.
"But we do want to have tariff-free, red tape-free access to the single market."
The European Commission said it is prepared for the negotiations to start as soon as the UK is ready but refused to give a date.
Spokesman Alexander Winterstein said: "We are fully prepared and ready for negotiations to start."
But he could not say when contacts would move "from talks about talks to more detailed talks".
He said: "This doesn't depend entirely on us. We are fully prepared."
Asked if concerns had been raised about the prospect of a tie-up with the DUP affecting the political process in the North, Mr Winterstein said: "The UK is a core guarantor of the Good Friday Agreement.
"As to the process of putting a government together in the UK, there is obviously an ongoing political process unfolding in the UK, the outcome of which we are respectfully awaiting."
Mr Barnier is set to update Europe's senior officials at a meeting of the college of commissioners on Tuesday.
Mrs May's official spokesman said the Prime Minister remained committed to securing "the best possible deal for the whole of the UK".
"The plan has been set out clearly in a number of ways in recent times," he told a Westminster media briefing. "Obviously there will be discussions in Cabinet, but the Secretary of State said we have set our plans out clearly."
Asked whether Mrs May still believed leaving without a deal would be better than agreeing a bad deal, the spokesman said: "We are confident of securing a deal which is good for the whole of the UK. You obviously wouldn't want to accept a deal which is worse than leaving without a deal."