Amber Rudd said crashing out of the EU without an agreement would be "far worse" than leaving with one, as the Office for National Statistics (ONS) reported how the labour market fared during the April-June period, with the the economy shrinking for the first time in seven years.
The data showed the jobless total climbed by 31,000 to 1.33 million, the biggest rise since 2017, while the unemployment rate ticked higher from 3.8% to 3.9%.
However wage growth - excluding bonuses - rose to 3.9%, a fresh 11-year high - though this was partly attributed to a change in the timing of pay rises for public sector health workers.
There was also a solid rise of 115,000 on the number of people in work to a new record high of 32.81 million.
The figures cover a period when UK GDP shrank by 0.2%, a downturn partly blamed on Brexit uncertainty.
Britain's labour market has proven resilient so far in the face of a slowing economy, with the unemployment rate running at its lowest level since the 1970s - though some economists saw signs of this strength fading in the latest figures, and warned this could worsen if there is a no-deal Brexit.
Ms Rudd also signalled concerns about such a scenario, saying: "A no-deal Brexit is definitely going to be a challenge for the economy, which is why the government is putting together so much preparation should it come to that, and we are very clearly focused as a government that we want to get a deal.
"A no-deal Brexit would be far worse than a deal Brexit, which is why the government is so focused on trying to get that.
"But we are also putting in place a lot of preparation to make sure that, should it come to that, we will have done all we can to mitigate against any difficulties."
Asked if she could guarantee that no-one would lose their jobs as a result of a no-deal Brexit, Ms Rudd said: "Listen, there are no guarantees about jobs, in or out, under any economic circumstances."
Tej Parikh, chief economist at the Institute of Directors, said: "The jobs market remains a source of strength for the UK economy, though it may now be reaching its peak."
Separate figures from the ONS also showed productivity falling by 0.6% in the period, apparently chiming with the view that the growth in jobs is partly thanks to employers preferring to hire workers they can later lay off rather than making longer-term commitments to investment.
Ian Stewart, chief economist at Deloitte said the figures showed the economy still had "momentum".
He added: "The days of sharply falling unemployment are behind us, but a tight labour market points to further gains in wages and spending power."
Chancellor Sajid Javid said wages were rising at the "fastest pace in more than a decade."
He said: "Thanks to the hard work of the British people and the government, we can further invest in our public services.
"And today's figures are another sign that despite the challenges across the global economy, the fundamentals of the British economy are strong as we prepare to leave the EU."
Andrew Hart, Economist at Capital Economics said the labour market appears to have shrugged off the contraction in Britain's economy in the previous quarter but warned that leaving the EU without an agreement will lead to further rise in unemployment.
He said: "The hit to demand a no-deal Brexit would deliver would see the labour market unwind somewhat, justifying interest rate cuts."