Downing Street has declined to endorse Liam Fox’s claim that British businesses are “lazy and too fat” to succeed at exporting, saying there should be a positive approach to seizing trade opportunities.

Theresa May believes the government needs to make sure it is doing enough to work with businesses that want to export, her spokeswoman said on Monday.

“I think the prime minister wants to make sure the government is looking at how we can create opportunities for British businesses overseas, taking forward some of the work done by the last government,” she said. “We will be looking at how we work up and down the country to identify with businesses where their opportunities are, to look at how trade missions overseas can work and ministerial engagement. I think this government is clear there are opportunities ahead and we should be approaching that in a positive manner.”

Asked if May agreed with her trade secretary that businesses are fat and lazy, the spokeswoman said: “I think the way the PM thinks about this is how do we make sure that British businesses are seizing the opportunities that exist and incentivising them to do that.”

The comments come as the Treasury prepares to meet exporters and importers for a “roundtable” discussion ahead of the autumn statement.

Last week, the prime minister delivered a slapdown to another of her ministers, after David Davis said it would be unlikely for Britain to stay in the single market following Brexit negotiations. May’s spokeswoman swiftly made it clear that this was Davis’s personal view, rather than government policy, and Britain should pursue the best deal possible.

Fox, meanwhile, made his controversial remarks at a Conservative Way Forward event for business leaders in parliament.

A former GP and staunch Eurosceptic, he suggested that business executives would rather play golf on a Friday afternoon than negotiate export deals.

“If you want to share in the prosperity of our country, you have a duty to contribute to the prosperity of our country,” Fox said. “This country is not the free-trading nation that it once was. We have become too lazy, and too fat on our successes in previous generations.

“What is the point of us reshaping global trade, what is the point of us going out and looking for new markets for the United Kingdom, if we don’t have the exporters to fill those markets?“We’ve got to change the culture in our country. People have got to stop thinking about exporting as an opportunity and start thinking about it as a duty – companies who could be contributing to our national prosperity, but choose not to because it might be too difficult or too time-consuming, or because they can’t play golf on a Friday afternoon.”

Fox resigned as defence secretary under David Cameron over questions about access given to his friend and unofficial adviser Adam Werritty.

However, May gave him the post of international trade secretary in her government, as one of several high-profile Brexiters handed responsibility for dealing with the fallout of the vote to leave the EU.

In comments that appear at odds with May’s stated commitment to an active industrial policy, Fox also argued: “We must turn our backs on [those] that tell us: it’s OK, you can protect bits of your industry, bits of your economy and no one will notice. It is untrue.

“Protectionism has always ended in tears. We must be unreconstructed, unapologetic free traders.”