The Conservative-Liberal Democrat run administration confirmed the increase includes 2% specifically to fund adult social care.
Chris Steward said it was the best option to protect frontline services but the Labour group said the proposals required further scrutiny.
The rise does not include the police and fire service charges.
The council said it planned savings of £6.5m in 2016/17 with a total budget of £117.9m.
It said its principal support grant from central government had dropped by £8.0m or 17% compared with 2015/2016.
Chris Steward, the council's leader, said: "We have been clear that we wish to protect the most vulnerable and focus on frontline services.
"We have therefore decided to take the adult social care precept as in this directorate we want to ensure people get well looked after."
The social care precept was announced as an option for councils in the comprehensive spending review in November.
Mr Steward has previously criticised the Labour group, who ran the council until May 2015, for increasing council tax, but said circumstances were different.
Neil Barnes, Labour spokesperson for finance and performance, said: "It is clear the coalition has benefited through Labour's sensible management of the council's finances until last year, evidenced in the relatively low level of savings it is having to make."
He said despite raising taxes the council was still planning to cut services people relied on.
A 3% rise on a typical Band D property in the city will amount to an increase of around £35.00 a year from April.
A final decision on the budget will be taken by the full council on 25 February.
Council tax in York is set to rise by 3% in April, the council leader has said.