Bpost raised its offer for its Dutch rival late on Sunday, offering to assume its pension liabilities in a deal that it said would create a company better placed to weather declining mail volumes.
Bpost described the offer, valuing PostNL at about 2.5 billion euros ($2.77 billion) as "friendly", though the Dutch company said on Monday that the offer was "unsolicited", adding that the companies were not in talks.
"We have confidence in our stand alone strategy," said PostNL in a statement, adding that it was considering the proposal "in accordance with its fiduciary duties".
Shares in PostNL rose 7.9 percent in early trading on Monday, while Bpost shares dipped 0.2 percent.
The offer, a mix of cash and shares equivalent in value to 5.65 euros per PostNL share, represented a 31.6 percent premium over PostNL's share price at the end of October, bpost said.
PostNL beat expectations in the third quarter, with cash operating income at 27 million euros, well ahead of the 18.7 million euros expected by analysts polled for Reuters, despite revenues that were barely changed at 770 million euros, the company said on Monday.
Earlier talks between the two companies foundered in late May, with media reports suggesting concerns over PostNL's pension liabilities had been a sticking point.
"The combination of our companies enables us to become one of the leading players in Europe," with 28 million potential customers across the Netherlands and Belgium, bpost Chief Executive Koen van Germen said in Sunday's statement.
Both companies face shrinking mail deliveries while domestic parcel deliveries are increasing due to online shopping. Some 3,200 new jobs could be created in a combined parcels business over the medium term, bpost said.
PostNL shareholders would own some 21 percent of the combined company if the transaction took place, bpost said, while the Belgian state's stake would fall from 51 percent to about 40 percent.
Reporting by Thomas Escritt; editing by David Clarke and Louise Heavens