JACKSON (AP) — House and Senate negotiators late Tuesday agreed on a plan to restore $82 million in cuts made to the current budget.

Gov. Haley Barbour has cut $458.5 million from what was nearly a $6 billion budget when the fiscal year started July 1.

The compromise agreed upon would restore over $37 million to K-12 education, including $2 million for National Board Certified teachers, $4 million to mental health, $1.7 million to public safety and a total of $16 million to the Department of Corrections.

Another part of the deal includes Barbour adding an extra $4 million to community and junior colleges from his discretionary fund.

‘‘The House and Senate conferees have reached an agreement on the fiscal year 2010 budget that the governor can live with,’’ said Dan Turner, Barbour’s press secretary. ‘‘It’s not the way the governor would have done it, but it’s a suitable compromise.’’

‘‘This bipartisan agreement with the House conferees has taken a lot of hard work and time but it has been worth the fight,’’ said Lt. Gov. Phil Bryant.

‘‘SB 2495 makes it possible for us now to continue crafting a fiscal 2011 budget resolution.’’

The full House and Senate still must agree on the plan before the cuts can be restored.