Novo Nordisk said it made an initial offer in December and then raised it, but that it had been rejected by Ablynx's management.
"Novo Nordisk encourages Ablynx's Board of Directors to engage in a negotiated transaction for the benefit of all stakeholders," the Danish firm said in a statement.
The initial offer of 26.75 euros in cash was raised to 28 euros per share in cash plus up to another 2.50 euros per share depending on performance.
Ablynx said in a statement that its board "concluded that the proposal fundamentally undervalues Ablynx and its strong prospects for continued growth..."
Ablynx specialises in the development of nanobodies: small fragments of antibodies that like larger antibodies can bind onto the antigens that cause an immune system response.
Novo Nordisk said its strong global haematology franchise would make it able to better develop one of those nanobodies, caplacizumab, which aims to treat a certain type of blood clots.
It called its buyout offer a "compelling opportunity and provides the clearest path to realizing full potential of Ablynx's portfolio in the best interests of all stakeholders, including patients and physicians."
The offer is the largest ever by Novo Nordisk for another pharmaceutical firm, according to Bloomberg News. The firm accounts for nearly half of the global market for insulin, but is also present in other sectors such as hormone treatments and drugs to control haemophilia.
Its shares were down a quarter of a percent in trading on the Copenhagen stock exchange at 339.10 kroner.
Shares in Ablynx were suspended on Monday morning in Brussels at the request of the market regulator.