Mr McConnell, on a visit to St Mirin's primary in Glasgow on Monday, announced a package in which he expects to see action in education, sport, the churches and on marches.
He acknowledged that "there are no quick fixes or easy solutions". But he wanted positive action to "put sectarian attitudes into the dustbin of history".
St Mirin's commended itself to the First Minister because of its joint endeavours with the non-denominational Croftfoot primary. Pupils meet every week to take part in drama and sports, and field trips are also planned.
Such "twinning" arrangements are among five education initiatives in an 18-point plan unveiled by Mr McConnell. Guidance for schools on the benefits of collaboration between schools of different denominations, including a comprehensive list of twinning activities and contacts, will be released by the Scottish Executive in the middle of the year. This will be preceded by a national seminar in the spring.
HM Inspectorate of Education will produce a report later this year on anti-sectarian work in schools which will highlight good practice.
Other education moves include:
* support worth pound;100,000 this year for anti-sectarian projects in schools, including use of the national anti-sectarian education resource pack; the Executive will provide another pound;13,500 for youth work.
* involving 700 pupils in seven performances and workshops of the anti-sectarian play, Singing I'm No a Billy, He's a Tim.
* an anti-sectarian category in this year's Scottish Education Awards to raise the profile of the work done in schools.
* an Executive sum of pound;10,000 targeted at supporting anti-sectarian messages in college and university campuses.
All of the Executive's initiatives will be overseen by a task group to be set up early this year. It will be asked to come up with a progress report one year on.
Although Mr McConnell came in for criticism for failing to consult key players before making his announcements, that was about the only serious complaint he faced.
Ewan Aitken, education spokesperson for the Convention of Scottish Local Authorities, said it was "not helpful" to have found out about these plans in the Press. But he added: "Anything which helps people to understand, and to celebrate, difference is to be welcomed. These are productive proposals which have our support."
Steven Purcell, leader of Glasgow City Council, said there were many examples already of the kind of activities Mr McConnell wished to encourage. It was important, however, that they should be initiated from the bottom up and not imposed.
Michael McGrath, director of the Catholic Education Service, said they had already alerted the executive to examples of good practice involving Catholic and non-denominational schools.
Peter McLean, of the anti-bigotry charity Nil by Mouth, agreed schools should not shoulder responsibility for bigotry. Studies in Northern Ireland showed that children assume sectarian attitudes before they even start primary school.
Osama Saeed, of the Campaign for Muslim Schools, seized on the twinning proposals to say that such schools would be happy "joining hands with other schools in joint initiatives". It should allay fears of separation, he felt.