The Memphis-based company, which has a market value of almost $21 billion (£14.8 billion), had raised its offer for Smurfit Kappa in hopes of entering into merger talks. Smurfit Kappa had turned down a proposed face-to-face meeting this month, it said.

"We believe our revised proposal is responsive to the views of Smurfit Kappa shareholders and provides a sound basis upon which to secure a recommendation from Smurfit Kappa's board," International Paper's chairman and CEO Mark Sutton said in a statement after Smurfit rejected its second offer in a month.

Smurfit said its board had unanimously rejected the increased offer of 25.25 euros in cash and 0.3 new International Paper shares.

The offer valued Smurfit at 8.9 billion euros ($11 billion)based on International Paper's closing price on Friday. The Irish firm said that remained well below valuations in recent industry transactions.

"The Board is resolute in its belief that the best interests of the group's stakeholders are served by pursuing its future as an independent company," said Smurfit, which operates in 35 countries in Europe and the Americas.

Smurfit Kappa shares closed down 3.4 percent at 33.56 euros, though still about 17 percent higher than the level they were trading at before International Paper's initial approach.

RBC Capital Markets analyst Paul Quinn said the drop in shares could indicate that the situation was tilting in International Paper's favour.

International Paper has indicated it was willing to move quickly and cooperatively to engage with Smurfit.

International Paper's shares were up about 4 percent at $52.16 in afternoon trading on the New York Stock Exchange.

A merger would help International Paper diversify beyond North America and the company said it could generate annual synergies of at least $450 million at a one-off cost of $570 million.

Growth in consumer spending and online shopping have boosted demand for packaging in recent years.

But some analysts said International Paper should be careful about increasing its bid further, as savings from a potential deal could be limited.

"One of the primary concerns investors have had since the news about IP's initial approach broke was that the synergy opportunities weren't obvious given the lack of geographic overlap," said KeyBanc Capital Markets analyst Adam Josephson.

International Paper said expected savings from a deal with Smurfit would represent just 5 percent of Smurfit's sales, compared with the 8 percent to 12 percent of sales for the U.S. company's three most recent acquisitions.

(Additional reporting by Clara Denina in London and Ankit Ajmera and Sanjana Shivdas in Bengaluru; editing by Jason Neely and Sriraj Kalluvila)

By Padraic Halpin and Graham Fahy

Stocks treated in this article : International Paper Company, Smurfit Kappa Group Plc