Barack Obama has criticised the way the FBI revealed a new investigation of emails possibly linked to Hillary Clinton’s private server, a move that has rocked the US presidential election in its final stretch.

Opinion polls show the race between Clinton and Republican candidate Donald Trump tightening since FBI director James Comey’s bombshell announcement last Friday. One even gave Trump a one-point lead, though the Democrat remains the clear favourite.

Clinton's 'October surprise' helps Trump in polls – but will it affect election day? Read more

In his first public comments on the controversial decision, Obama told the online outlet NowThisNews: “I do think that there is a norm that when there are investigations, we don’t operate on innuendo. We don’t operate on incomplete information. We don’t operate on leaks. We operate based on concrete decisions that are made.

“When this was investigated thoroughly the last time, the conclusion of the FBI, the conclusion of the justice department, the conclusion of repeated congressional investigations was that she had made some mistakes but that there wasn’t anything there that was prosecutable.”

Comey said it was unclear whether the emails – reportedly found on the laptop of Clinton aide Huma Abedin’s estranged husband Anthony Weiner – are significant. His letter to Congress triggered a fierce backlash from Democrats and even some Republicans.

Obama said Clinton made an “honest mistake” by using a private email server as his secretary of state, something that was now “being blown up into just some crazy thing”. New voters hear “all that noise” and wonder whether they should be worried about Clinton’s conduct, he added, but he said he had absolute confidence in her.

Campaigning reached a new frenzy on Wednesday with less than a week until election day and early voting far in excess of the same stage in 2012. Trump was due to hold three rallies in Florida, the biggest prize, while Clinton was in Florida and Arizona, traditionally a Republican bastion. Other surrogates of both candidates were spread through the battleground states that will determine who wins the White House.

Speaking in Miami, Trump repeated familiar attacks on the media, this time singling out reporter Katy Tur of NBC, naming her four times. “These people are among the most dishonest people I’ve ever met, spoken to, done business with,” the celebrity businessman said. “There has never been anywhere near the media dishonesty like we’ve seen in this election.”

Trump, wearing a white “make America great again” baseball cap and standing in front of a giant US flag, cited a New York Post column that described the election as “the low watermark of journalism”. He complained bitterly: “We’ll have a great story, we’ll give it out to the media, they’ll make it look as bad as possible.”

Trump also mocked the New York Times for a drop in its earnings and insisted that his campaign was surging but not getting the coverage it deserves. “We have massive crowds. There’s something happening.”

Pointing to Tur, he continued: “They’re not reporting it. Katy, you’re not reporting it, Katy, but there’s something happening, Katy. There’s something happening, Katy.”

Trump has picked on Tur before. Last December he branded her “Little Katy”, described her as a “third-rate reporter” and said she should be fired.

On Wednesday the crowd turned on Tur, according to Holly Bailey, national correspondent of YahooNews. She tweeted: “Trump calls out @KatyTurNBC from the stage in the middle of a riff bashing media and now this guy behind me is just endlessly taunting her … ‘Do your job Katy! Report the truth Katy! Report what he says Katy!’”

Several journalists expressed support for Tur. Chris Cillizza of the Washington Post tweeted: “Bullying. And totally unacceptable for someone simply doing her job.”

During the rally Trump also made reference to two Iowa police officers ambushed and killed hours earlier. “An attack on our police is an attack on all of us,” he said. “Law enforcement is the line separating civilisation from total chaos. You have to remember that.”

Talking more broadly about violence against police, he said: “What it is is a lack of respect for our nation. It’s a lack of respect for our leadership. To all the great men and women of law enforcement, I want you know, we’re with you, we support you and we will stand by you. We’re going to restore law, order and justice in America. Justice.”

The crowd chanted: “U-S-A! U-S-A! U-S-A!”

Clinton’s campaign cancelled a Des Moines rally with vice-presidential candidate Tim Kaine and former president Bill Clinton in the wake of the killings.

Trump was introduced by Reince Priebus, chair of the Republican National Committee, who has stuck by the party nominee as others have fallen away. “We know Donald Trump is not politically correct,” he said. “And look at Hillary Clinton, who lies with incredible grace and skill. She lies over and over and over again, over and over again.”

A week ago Clinton was cruising to victory. That still seems the most likely outcome, especially given the mathematics of the electoral college. But Comey’s announcement panicked some Democrats and gave Republicans renewed momentum. On Tuesday a Washington Post/ABC poll showed Trump at 46% and Clinton at 45%. On Wednesday a CNN/ORC survey put Clinton at 49% and Trump at 47% among likely voters in Florida, while Clinton was four points up in Pennsylvania.

In a worrying sign for Clinton, early voting turnout for African American voters in swing states has fallen from 2012. In North Carolina, black turnout is down 16% from this point in 2012, while white turnout is up 15%. In Florida, black voters’ share of the early voting turnout is 15%, 10 points lower than it was in 2012.

Obama said in an interview on the Tom Joyner Morning Show, which is aimed at African Americans: “I’m going to be honest with you right now. The Latino vote is up. The overall vote is up. But the African American vote, right now, is not as solid as it needs to be.”

Obama has been more active on the trail that previous sitting presidents in a bid to protect his legacy. In Columbus, Ohio, on Tuesday night, he went further than before in tackling the question of whether Clinton is facing discrimination from some reluctant men. He said there was a reason why there has never been a female president in America’s 240-year history.

“And we have to ask ourselves, as men, because I hope my daughters are going to be able to be achieve anything they want to achieve,” Obama said. “And I know that my wife is not just my equal but my superior. And I want us – I want every man out there who’s voting – to kind of look inside yourself and ask yourself, if you’re having problems with this stuff, how much of it is that we’re just not used to it.”

He added: “So that you – when a guy’s ambitious and out in the public arena and working hard, well, that’s OK. But when a woman suddenly does the [same] – you’re like, why is she doing that? I’m just being honest. I want you to think about it because she is so much better qualified than the other guy. She has conducted herself so much better in public life than the other guy. Somehow this is hard to choose? It shouldn’t be!”

It is now all hands on deck for both candidates. Trump’s wife, Melania, will make her first solo appearance of the election in the Philadelphia suburbs on Thursday. The campaign said she will talk about the “kind of dedicated, strong and committed first lady” she would be. It will be her first address since the Republican national convention in July, where she delivered a speech was partially plagiarised from first lady Michelle Obama.