It was Donald Trump’s first rally since Democrats launched an impeachment investigation – the first since he was accused of asking a foreign leader to dig up dirt on a rival.

The president had dismissed the accusations as a “witch hunt”, a conspiracy hatched by the media and political opponents to target him. To a person, his supporters echoed his words – sometimes literally.

“It’s just a lot of fake news, as Donald Trump would say,” said Sean Maguire, a small business owner who was was wearing a red Make America Great Again baseball cap, and carrying a large black umbrella, as he entered the rally amid a downpour. “Because it is a 100 per cent witch hunt. They have not let him be our president for the last three years. All they have tried to do is impeach him.”

In the three weeks since Nancy Pelosi seized the momentum by pressing the button on a formal impeachment investigation, polls show a growing number of Americans support the process. Among the most recent, one poll commissioned by conservative Fox News suggested 51 per cent supported removing him from office with just 40 per cent opposed. This earned a special rebuke from Mr Trump himself.

At the same time, while other data suggests independents and undecided voters may be less supportive of him, polls also show a hard core of unshifting support, no matter what he says, and no matter what anyone says about him.

Minneapolis protesters clash with police outside Trump rally Show all 12 1 /12 Minneapolis protesters clash with police outside Trump rally Minneapolis protesters clash with police outside Trump rally IMAGES INCLUDE EXPLICIT LANGUAGE: Counter protesters confront horse-mounted law enforcement after a rally by U.S. President Donald Trump in Minneapolis, Minnesota. Reuters Minneapolis protesters clash with police outside Trump rally Anti-Trump protesters hold signs outside the Target Center in Minneapolis, Minnesota, ahead of a "Keep America Great" rally AFP/Getty Minneapolis protesters clash with police outside Trump rally A counter protester holds a sign before a rally by U.S. President Donald Trump in Minneapolis Reuters Minneapolis protesters clash with police outside Trump rally The state is home to some of the President’s most prominent critics – including senator Amy Klobuchar and congresswoman Ilhan Omar AFP/Getty Minneapolis protesters clash with police outside Trump rally Both the president’s backers and his detractors were, for the most part, kept separate EPA Minneapolis protesters clash with police outside Trump rally On the fringes of the action the president’s supporters clashed with protestors AP Minneapolis protesters clash with police outside Trump rally A protester with a whistle attempts to interrupt U.S. President Donald Trump while he spoke Getty Minneapolis protesters clash with police outside Trump rally Minneapolis Police create a blockade to hold back protestors Getty Minneapolis protesters clash with police outside Trump rally On the arrival of the police protestors could be seen jeering and hurling projectiles at officers AP Minneapolis protesters clash with police outside Trump rally Officers deployed pepper spray during the protests AP Minneapolis protesters clash with police outside Trump rally Baby Trump balloons are carried by a counter protester before the rally Reuters Minneapolis protesters clash with police outside Trump rally Anti-Trump protesters hold signs outside the Target Center in Minneapolis, Minnesota AFP/Getty

The website FiveThirtyEight, which tracks five different polls, shows approval for the president remains around 42 per cent, and has done since he entered office. His disapproval rating is around 53 per cent.

“I think – though Democrats might not agree – if the situation was reversed, we’d see the same with the Democratic Party,” said Eric Ostermeier, a research fellow at the University of Minnesota who publishes the Smart Politics blog about politics in the state. “And that is the by-product of the extreme polarisation that has befallen our country.”

He said in a two-party system, where voters found the other option “too abhorrent”, they chose to go with their own party’s candidate and “dig in and dig in”.

“Given everything that has happened to his administration, what I think is very telling, is [his base of support] has not moved more than a few inches. Here in Minnesota it has also been pretty consistent; it was 46 when he was inaugurated, and it’s 43 now. Some of his negatives have risen, but those who support him have remained relatively stable.”

Natalie Zeleznikar would almost certainly consider herself a hardcore supporter. The owner of an assisted living facility in Duluth in the north of the state, she was also trying to avoid the rain, as she entered the rally on Thursday afternoon.

She claimed Mr Trump had encouraged people to feel patriotic, which she said was important. “At the centre I run, we say the pledge of allegiance every morning, and it means a lot to people.”

“It’s important to honour what we stand for and believe in something. If you don’t stand for something, you stand for nothing,” she added.

Trump launches blistering attack on Ilhan Omar by repeating conspiracy theories from right-wing blog

“Whether you love him or hate him, he believes in something and that’s why you see everybody here today. He has a strong sense of what he believes in.”

On the issue of impeachment, she said all the facts had not come out, but that “personally no, he should not be impeached. From what I see as facts, I don’t have reason to think it’s impeachable”.

Different people said they admired the president for different reasons. One woman, Brenda Muth, who drove for two hours from her farm in Mason City, Iowa, said he was good for farmers and she liked the way he had confronted China on trade.

David Larson, a business owner from Minneapolis, who was attending because his 17-year-old granddaughter wanted to, did not like Mr Trump’s swagger as a reality television personality. However, since becoming president he had done – or tried to do – everything he vowed to as a candidate, he said.

Inside the Target Centre, home to the Minnesota Timberwolves professional basketball team, rock music pumped from the speaker. The Rolling Stones’ Angie, and Prince’s Purple Rain – played in defiance of the requests of the Minneapolis icon’s estate. Most curious in its ability to lodge in the brain, was Lee Greenwood’s 1984 hit God Bless the USA, the lyrics to which say “I’m proud to be an American/ Where at least I know I’m free/ And I won’t forget the men who died/ Who gave that right to me”.

Matt Erlien, who was seated with his wife, Merliza, originally from the Philippines, said he supported Mr Trump because he was opposed to abortion. He said he also supported his hardline approach to immigration.

“I think it’s fair. A lot of people get to come here illegally and that means other people don’t get to come,” he said. “I think it’s a fair system, just obeying the law.”

Two military veterans, Marvin Werth and Kerry Murphy, were also veterans of Donald Trump rallies. Mr Murphy had been to seven, and his friend to three. They spoke about seeing Mr Trump in religious terms, likening the experience of being surrounded by 20,000 similarly-minded people to a revivalist church gathering.

During his raucous address, after the songs had stopped playing, and after the crowd had been warmed up by his son, Eric Trump, and vice president Mike Pence, the president launched into a blistering attack on local congresswoman Ilhan Omar, accusing her of being anti-American and antisemitic. He also borrowed from a right-wing trope to accuse her, without evidence, of marrying her brother – something she has denied.

“Congresswoman Omar is an American-hating socialist. How do you have such a person representing you in Minnesota,” he said. “She is a disgrace to our country.”

He also claimed Minneapolis had permitted too many Somali immigrants to settle there, and won loud applause when he bragged of his decision to cut the number of refugees the US accepts by 85 per cent.

Other than the police officers, cleaners and people working at the fast-food outlet, the overwhelming majority of people in the venue were white, middle aged and lived in the rural areas and suburbs surrounding Minneapolis, rather than the city itself, which has long been a Democratic stronghold.

Michael Adams was not any these things. A black, 55-year-old professional who lived in Minneapolis, he said he could not judge whether Mr Trump was racist. Yet he said that as a person of colour, there was nothing the president said that upset him.

“I do not feel that way, and he has not said anything to make me feel that way,” he said. “Sending a strong message to the radicals around the world may [make people say] he’s racist, but he’s done nothing to make me feel as if he is a racist.”

It was not just supporters of the president who flocked to the centre of Minneapolis. Several hundred protesters gathered to hold placards denouncing Mr Trump and blowing on whistles to symbolise the whistleblower complaint.

Among the demonstrators heading home on the train was Khadija Isee, a 25-year woman who had come to the country from Somalia. She had heard what Mr Trump had said about her community and she was upset.