ST. PAUL — Minnesota has extended a new offer to Wisconsin on income tax reciprocity.

An agreement would simplify income taxes for those who live in one state and work in the other. Minnesota officials have offered to lower Wisconsin’s annual payment by $1 million if the state approves the agreement by Sept. 30.

Reports said some 80,000 residents who live in one state and work in the other have had to file income taxes in both states since the 40-year-old deal between the two states lapsed in 2009.

Minnesota said Wisconsin owes it about $92 million a year because many more Wisconsinites work in Minnesota than the other way around. That’s $4 million to $6 million more than Wisconsin officials think the state should pay. Wisconsin revenue officials so far have rebuffed the offer.