The “entire machinery of government” is focused on getting a Brexit deal with the EU, says Priti Patel.
The home secretary said Boris Johnson was “fully committed” to negotiating an agreement by the 31 October deadline.
But when pressed by the BBC’s Andrew Marr to reveal details, she said it wasn’t “a public negotiation”.
Earlier, Mr Johnson said the UK would break out of its “manacles” like cartoon character The Incredible Hulk, in order to leave the EU.
He told the Mail on Sunday: “Hulk always escaped, no matter how tightly bound in he seemed to be – and that is the case for this country.
“We will come out on 31 October and we will get it done.”
The prime minister said on Friday that he was “cautiously optimistic” of getting a Brexit deal, but the UK would leave by the deadline “whatever happens”.
This is despite MPs passing a new law that would force the prime minister to ask the EU for an extension to that deadline if a deal wasn’t agreed by 19 October – two days after a key EU summit.
Mr Johnson is due to meet European Commission president Jean-Claude Juncker in Luxembourg this week as negotiations continue.
Brexit Secretary Steve Barclay said a “landing zone” was in sight for an agreement with the EU, and a “huge amount has been happening behind the scenes”.
But he told Sky News’ Sophy Ridge programme said there was still “significant work” to do.
What’s the deal?
Ms Patel told Andrew Marr: “The prime minister is fully committed to getting a deal.
“I hope the country has heard [Mr Johnson’s] sheer commitment and determination to ensure that we leave on 31 October, and also that the entire machinery of government now is focused on getting that deal and is planning and preparing to leave with a deal.”
She added: “My instinct is we have to leave, and we have to leave with a deal on 31 October.”
But there are still questions as to what that deal will be, after the EU’s chief Brexit negotiator Michel Barnier said he did not have “reasons to be optimistic” over coming to an agreement with the UK.
Reports suggested Mr Johnson and his team were considering a plan to keep Northern Ireland more closely aligned to the EU after Brexit, which they hoped would remove the need for the Irish backstop – the policy in the existing withdrawal agreement to prevent a hard border returning to the island of Ireland.
But the Democratic Unionist Party – which supports the Conservatives in Parliament – rejected any plan that would see Northern Ireland treated differently to the rest of the UK.
Ms Patel was a vociferous opponent of the backstop when Theresa May was prime minister – voting against her deal three times – and took the same line as the DUP.
But pushed on the reported alternative, she said: “We are working through that right now.
“I am not going to pre-empt any of the discussions right now in terms of acceptability [of that plan].”
The home secretary added: “We are in different territory right now. There’s no point arguing about the past.
“We are moving forward now… as a government, collectively focussed on leaving but leaving with a deal.”