KPN's shares have lost more than 70 percent of their value since Blok took the top job at the Netherland's largest telecommunications company in 2011. Customers with smartphones have been ditching KPN for cheaper Internet-based communications services such as WhatsApp and Skype.
KPN responded by hiking its prices for mobile Internet access, but was still forced to issue new shares this year to shore up its balance sheet. This month it also sold its German division, E-Plus, for around $11.4 billion, to Telefonica SA of Spain.
Blok had initially agreed to sell E-Plus for around $10.4 billion, but later negotiated a better deal under pressure from Movil.
"We have plenty of money because of the E-Plus sale, and for the moment we will continue independently," Blok said Thursday.
KPN is due to report third quarter earnings on Wednesday.
"KPN shareholders were better off with the Movil offer and they are now stuck with a company that's not worth more than around 2 euros per share," said Theodoor Gilissen analyst Jos Versteeg in a note.
He predicted Slim will eventually re-bid for KPN, possibly after buying additional shares below the 2.40 offer price.