Alex Salmond said he had listened to concerns that the new law was being rushed through parliament.
He said he would set a new timetable to ensure it was passed by the end of the year.
Opposition parties, Celtic and Rangers football clubs and the Church of Scotland had all expressed concern at the original timescale.
The bill was introduced to parliament just last week and ministers had wanted to see it passed by the end of the month, in time for the start of the new football season in July.
The Scottish Parliament's justice committee expressed concern over the speed with which the bill was to go through.
Mr Salmond announced the delay to the Offensive Behaviour at Football and Threatening Communications Bill during first minister's questions, at Holyrood.
He told parliament more time was needed to take a range of evidence and views on the proposals.
Mr Salmond said: "I accept, and I think everybody accepts, we have a majority in this chamber - but we need consensus.
"I hope, because what we say in this place on this issue has huge ramifications across society, that we can allow for the probability, the certainty, that each and every single one of us wants to eliminate sectarianism and sectarian displays from Scottish football.
"Each and every one of us wants to eliminate sectarianism from Scottish society.
"I hope that parliament will accept there is a huge, genuine urgency in this matter, and also accept that this government wants to achieve the consensus within parliament and throughout Scottish society."
Continue reading the main storyTwo new offences on football-related behaviour regarded as offensive and threatening.
One deals with disorder around football matches inside the ground, and extends to those travelling to and from stadiums - as well as fans watching games elsewhere, for example in pubs or on big screens outdoors.
The second offence deals with serious threats - including murder - made on the internet.
That would take in posts on sites like Facebook and Twitter, as well as specific websites.
Both offences would become indictable, with a maximum punishment of five years in jail.
The maximum jail term for sectarian hate crimes is currently six months.
Decisions on sentencing in each case are a matter for the courts.
The bill aims to stamp out abusive behaviour from football fans, whether they are watching matches in a stadium, in the pub or commenting online.It would raise the maximum jail term from six months to five years.
The new legislation comes in the wake of several high-profile football-related incidents.
These include trouble at Rangers/Celtic games and the sending of suspected bombs to Celtic manager Neil Lennon and two other high-profile supporters of the club.
Rangers and Celtic football clubs both earlier warned the laws risked being flawed if they were rushed through.
Celtic previously raised concern that the club was given only four days to consider the legislation, while Rangers had said that the desire to have the legislation in place for the new football season brought the risk that it might be flawed.
Cameron Ritchie, president of the Law Society of Scotland, welcomed Mr Salmond's decision, adding: "On such an important issue as this, we need effective law that is both workable and not open to challenge."
Opposition parties welcomed the Scottish government's move.
Labour leader Iain Gray, said: "The first minister and SNP's incompetence had undermined the credibility of the bill and they have now had to climb down from their attempt to rush it through."
The Lib Dems' Willie Rennie, who thanked the first minister for his decision, said: "Scores of questions still remain over the bill and we will work constructively with the Scottish government to explore these issues."
Annabel Goldie, the Conservative leader, added: "The Scottish government has showed some much needed common sense and humility in acknowledging the wide ranging concern about this bill as currently drafted, the lack of consultation and the clear possibility of negative, unintended consequences."
Two Christian organisations - the Christian Institute and Care for Scotland - said they were dropping legal action which aimed to force the Scottish government to take more time over the legislation.
The Offensive Behaviour at Football and Threatening Communications Bill has now passed its first hurdle at Holyrood, with the SNP and Labour voting for it, the Liberal Democrats voting against and the Tories and Greens abstaining.
The legislation will now move forward to the next stage of parliamentary scrutiny.
The tram project is behind schedule and over budget First Minister Alex Salmond has given his backing to a public inquiry into the handling of the Edinburgh trams project.