Entra said an offer may instead emerge from a different bidder, sending the company's shares soaring.
"While the board appreciates the interest ... the potential offer will not be recommended," Entra said of SBB's bid.
"Prior to today's offer from SBB, (Entra) has received a separate non-binding proposal from another party that may or may not lead to an offer," the Oslo-listed firm said in a statement.
In a sign that investors expect more bids to come, Entra's share price surged 20.5% to 173.2 Norwegian crowns, more than SBB's valuation of 165 crowns.
Shares in SBB fell 3.4% to 28.20 Swedish crowns by 1305 GMT.
Entra's assets include the 26-storey Posthuset office block in Oslo, the Norwegian capital's second tallest building.
SBB said its proposed takeover would create the largest listed real estate company in northern Europe and give increased stock market liquidity and access to capital.
"SBB has chosen to publish its intention to launch an offer with the aim to provide Entra's shareholders with an opportunity to accept the offer prior to year-end," the Swedish company said.
SBB has identified potential annual savings of 260 million Swedish crowns ($30.2 million) from a merger, of which 60 million would come from operations and 200 million from lower funding costs for the combined company, it said.
SBB's bid consisted of a cash portion of 115.5 crowns per Entra share as well as new shares in SBB worth 49.5 crowns each, representing a premium of 14.8% to Entra's closing share price on Nov. 23, the Swedish company said.
Citigroup, Goldman Sachs and Arctic Securities were advising SBB, while Entra said it had contracted ABG Sundal Collier to work on its behalf.
($1 = 8.9874 Norwegian crowns)
($1 = 8.6000 Swedish crowns)
(Reporting by Terje Solsvik; editing by Jason Neely, Jane Merriman and Susan Fenton)
By Terje Solsvik