The paper faced criticism, along with its sister paper The Sun, for not featuring on its front page the story that an inquest jury had ruled that 96 Liverpool fans who died in the 1989 tragedy were unlawfully killed.
In a statement posted on Twitter, the paper said: “The Times led with Hillsborough coverage on all our digital editions throughout the day.
“This morning we have covered it extensively in the paper with two spreads, the back page, a top leader and an interactive on the victims.
“We made a mistake with the front page of our first edition, and we fixed it for the second edition.”
A photo of the families outside the Warrington courtroom appeared on the front of later editions of The Times, along with a trailer for its coverage which ran to several pages, including an editorial comment.
Times editor John Witherow told the Guardian: “We made a mistake. We put it right.”
The Sun came in for particular criticism, having run a front page story proclaiming to tell “The Truth” four days after the disaster.
The article featured claims from an anonymous policeman that some fans had “picked pockets of victims”, “urinated on cops” and that some beat up a policeman who was giving the “kiss of life”.
Despite not covering the verdict of the two-year inquest on the front page, which cleared the fans of any fault, the paper ran a double-page spread on the outcome, and covered it in its main leader.
Kelvin MacKenzie, the paper’s former editor who oversaw the story published in 1989 blaming fans, insisted he had been “duped”.
He told the BBC: “I was appalled to discover the police had been lying for 27 years. Absolute shock at the manner in which the evidence, when you study the evidence during the two years, it was simply appalling.
“I was completely duped - it came from an agency. They said they were senior police officers, they said it was the head of the ambulance service, they said it was a Tory MP. They all said it was the fans.
“It’s quite clear today the fans had nothing to do with it. It was an absolute shocker, absolute shocker for me personally but also the only people that really matter, of course, are the victims and their families who exist today. My heart goes out to them.”
Asked if The Sun should have run the story on Wednesday’s front page, he said: “That’s not a decision for me, I’m not the editor of the paper. He’s a very successful guy, former editor of the Daily Telegraph. He makes pretty good decisions but that is up to him.”
The Sun’s leader on Wednesday stated that, after 27 years, the “Hillsborough families finally have their first measure of justice”.
It added: “Whether they get more is in the hands of the CPS. We hope they do.
“The horror that befell Liverpool fans was, as the inquest has now found, the fault of catastrophic police blunders - specifically by former Chief Superintendent David Duckenfield - which were shamefully then covered up.
“Failures by the ambulance service were also to blame, as was the design of the Sheffield stadium.
“The supporters were not to blame. But the police smeared them with a pack of lies which in 1989 The Sun and others in the media swallowed whole.
“We apologised prominently 12 years ago, again four years ago on the front page, and do so unreservedly again now.
“Further, we pay tribute to the admirable tenacity of the friends and relatives over so many years on behalf of the 96 who died.”
The absence of coverage of the Hillsborough inquest on Wednesday’s front page led to criticism of the paper, with many on Twitter voicing their opinions.
Impressionist and comedian Rory Bremner tweeted that the relegation of the story to pages eight and nine was “extraordinary”.
On Tuesday night “The Sun” became a trending topic on Twitter in the United Kingdom, with more than 124,000 tweets using the term.
Actor Stephen Mangan described the decision as “disgraceful”, adding: “Wait - neither @TheSun nor @thetimes mention Hillsborough on their front pages?!”
In 2012 The Sun ran a front page called “The Real Truth” in which the paper announced they were “profoundly sorry for false reports”.
On Tuesday, Mr MacKenzie said: “As I have said before, the headline I published was wrong and I am profoundly sorry for the hurt it caused.”
Talking on Sky News’s press preview, The Sun’s political editor Tom Newton Dunn said the police are at the “core” of the whole story and the paper was misled by them.
He said if people are still angry over the 1989 front page he “completely understands”, adding: “We deserve everything that is thrown our way.”