Jeremy Hunt has called warnings from Airbus about the UK’s Brexit strategy “completely inappropriate”, saying the government should ignore “siren voices”.

In the most bullish comments from a cabinet minister since the intervention by the aerospace company’s chief executive, Hunt said businesses sounding the alarm about job losses risked undermining the government at a key moment in the negotiations.

“It was completely inappropriate for businesses to be making these kinds of threats, for one simple reason,” the health secretary told the BBC’s The Andrew Marr Show on Sunday. “We are in a critical moment in the Brexit discussions. We need to get behind Theresa May to deliver the best possible Brexit, a clean Brexit.”

Hunt said the best way for businesses to achieve the “clarity and certainty” they needed was to back the prime minister in her negotiations with Brussels. “The more we undermine Theresa May, the more likely we are to end up with a fudge, which would be an absolute disaster for everyone,” he said.

His comments were echoed by the international trade secretary, Liam Fox, who said the UK’s negotiating position was being undermined by those urging the government to take “no deal” off the table.

“If we actually say we’ll accept any deal you give us rather than walk away, that weakens our negotiating position,” he told Sky’s Sophy Ridge on Sunday. “And people who are making these comments need to understand that they may be actually putting the UK at a disadvantage by making these cases.”

Over the weekend, BMW followed Airbus in warning about the consequences of Brexit uncertainty, saying the carmaker needed clarity on customs arrangements within months. Airbus, which employs 14,000 people in the UK, has said a no-deal scenario directly threatens its future in the country.

Further pressure came as the biggest business groups in the UK wrote a stinging letter to the prime minister, as well as to the European council president, Donald Tusk, and the European commission president, Jean-Claude Juncker, on Sunday, demanding greater input for business in the negotiations.

Business leaders have been further angered by reports that the foreign secretary, Boris Johnson, allegedly responded to a question about companies’ Brexit concerns at a diplomatic reception this month by saying: “Fuck business.”

Hunt said it was not surprising there was concern from businesses about the impact of Brexit, but it was not in the interests of the European commission to say the negotiations were going well. “That’s part of their negotiating tactics,” he said.

“We have to ignore these siren voices … get on and support Theresa May. If you look at the approach Theresa May has taken to Brexit so far, she has the instincts of a Brexiteer but the cautious pragmatism of a remainer, which is where I think the British people are. She brings incredible resilience and we have to allow her to get on and negotiate this deal.”

The CBI’s deputy director, Joshua Hardie, hit back at Hunt’s remarks on Twitter:

Former minister Digby Jones, a Brexit supporter, also sounded a note of caution about the need to secure an acceptable exit deal.

“If ... we are at civil war in Britain, which we are, and at the same time you’ve got an EU who, or should I say Germany, who are going to play this right the way down to midnight on 29 March – why wouldn’t they – then what you’ve got is, yes you’re right, falling off the edge will be a catastrophe,” he told BBC Radio 5 Live.

In his interview, Hunt also dismissed criticism of government claims that a £20bn a year NHS spending increase would come partly from a “Brexit dividend”, which the Institute for Fiscal Studies has said does not exist, given economic forecasts about the impact on growth of leaving the EU.

He said there would not be very much extra cash by the time Britain leaves the EU in 2019, given the financial settlement with Brussels. “Going forward, we will have settled that,” he said. “A lot of those experts have been proved wrong before in their forecasts and we actually think the British economy can get through this very challenging period, but we don’t know exactly when and what the impact will be.”

The Liberal Democrat Brexit spokesman, Tom Brake, said Hunt’s comments were “calibrated more to appeal to his Brexiteer colleagues than to reflect reality”, and businesses were right to speak out.

“Whilst the Conservatives may wish to ignore reality and pat each other on the back after two years of achieving precisely nothing in the Brexit negotiations, they cannot expect businesses to act in the same way.”

The intervention by businesses comes ahead of this week’s European council summit, where May is under pressure to show some progress on customs arrangments and the Irish border. Karen Bradley, the Northern Ireland secretary, will meet chief negotiator Michel Barnier in Brussels on Monday and meet MEPs.

Bradley said she would reiterate the UK government’s commitment to securing a Brexit deal that would avoid a hard border.

“We are confident that we will secure a good deal for the whole of the UK, and we are working towards finalising this with the EU in autumn,” she said.

“As we do, we will ensure that our departure from the EU does not do anything to set back the historic progress we have made in Northern Ireland over the past 20 years, and that the Belfast agreement is protected in all its parts. This is the message I will be reinforcing during my meetings today.”