The suggested cap is lower than an earlier 7.4 percent request, but more than two times the 1.77 percent cap set by the city.
The property tax levy to support Minneapolis schools will rise by no more than 4 percent next year.
The school board unanimously approved the levy cap on Tuesday. It is down sharply from the 7.4 percent proposal made by district staff members earlier this month but is still the highest increase of the city's major taxing jurisdictions.
Board members had questioned the staff recommendation, citing the sluggish state of the economy, and could cut it further when the levy is set in December.
The proposed increase would cost the owner of a house near the city median value of $171,000 about $61 more, down from $90 in the original proposal. Hennepin County set a 1 percent levy increase cap and the city a 1.77 percent cap on the levy increase for 2013.
The reduced school levy means that the district will have to dip more into savings or into other programs to pay its annual $6 million bill for a closed pension plan for nonteaching employees. Only $1 million would be levied for that pension bill.
The tighter cap also means that the district will scale back to spending $45 million annually on planned renovations of aging schools. That's a $5 million annual cut. A program to expand or reopen buildings would start at $5 million in 2013 and the following year, then rise to $15 million in the following two years. Potential projects include reopening Webster and Cooper schools, as well as improving the Howe playground and the cafeteria at Pillsbury.