"IP believes the revised proposal was highly attractive and formed a sound basis for engagement, which the company viewed as essential to determining the full value potential of the combination," the paper-packaging firm said in a statement.
International Paper has decided to end its pursuit after courting Smurfit for more than three months, according to people familiar with the matter.
Under Ireland's rules, Memphis-based International Paper will be barred from making a fresh attempt to buy Smurfit for 12 months once it has dropped its current approach.
The decision comes after the American company made two takeover proposals in February and March, both of which were rejected. The first valued Smurfit at 36.46 euros ($42.71) a share and the second at 37.54 euros per share, or 8.9 billion euros.
Smurfit Kappa had argued that it was better served pursuing its future as an independent company.
International Paper last month ruled out making a hostile bid for Smurfit and instead asked the Irish company to discuss its proposal.