Michelle Obama has said Donald Trump’s rise to power in the 2016 US election “still hurts” but she and her husband had “laid a marker in the sand” with his presidency.

The former first lady said “leadership matters” but ruled out the possibility of running for president herself in future.

In the run-up to the release of her new book, The Light We Carry, she spoke to BBC Breakfast about the political polarisation in the UK and US.

Asked about the American electorate’s decision to replace Barack Obama with Trump, she said it “still hurts”, and she sometimes questioned if her husband’s time in office had mattered.

“When I’m in my darkest moment … my most irrational place, I could say, well, maybe (it didn’t matter). Maybe we weren’t good enough.

“But then I look around when there is more clarity … and think more rationally, I think well … today there’s a whole world of young people who are thinking differently about themselves because of the work that we’ve done. And that’s where you can’t allow great to be the enemy of the good.

“You know, did everything get fixed in the eight years that we were there? Absolutely not. That’s not how change happens. But we laid a marker in the sand. We pushed the wheel forward a bit.

“But progress isn’t about a steady climb upward. There are ups and downs and stagnation. That’s the nature of change. And that’s why the work that we’re doing today is about empowering the next generation, the generation that we’re handing the baton over to and making space for them to make their mark on history.”

Obama said it was important to have leadership that “reflects the direction that we want to go in as a people” and that made the general public “feel seen”.

“Leadership matters,” she said. “The voices at the top matter if we can continue to be susceptible to voices that want to lead by fear and division. That’s why government matters, democracy matters. Voting matters. So I think it starts with having leadership that reflects the direction that we want to go in as a people.”

Asked what question she most disliked being asked, she said: “Are you going to run for president?’ I detest it.”

“I’m not going to run,” she added.