Hammerson has rebuffed a sweetened £5.04 billion takeover offer from Klepierre, saying the French firm's advances failed to reflect the value of the shopping centre giant.
Hammerson part-owns the Dundrum Town Centre, the Ilac Centre in Dublin city centre and the Pavilions in Swords in Co Dublin.
It knocked back the revised cash-and-shares bid of 635p - comprising 50% cash and 50% in new Klepierre shares, but said its board was willing discuss an offer that met its valuation.
The move comes after the group revealed last week that it would halt efforts to finalise a £3.4 billion tie-up with Intu as it awaited clarity on an approach from European suitor Klepierre.
Hammerson branded Klepierre's initial 615 pence cash-and-shares bid worth £4.88 billion "wholly inadequate" and "entirely opportunistic".
It said the offer price today did not justify further talks at this price, but the French rival still has until April 16 to table a formal offer.
"The board has considered the revised proposal from Klepierre carefully. At 635 pence, it is only a 3% increase on the previous proposal and continues very significantly to undervalue the company," David Tyler, Hammerson chairman said.
The upped proposal was outlined during crunch talks between Mr Tyler and Klepierre chairman Jean-Marc Jestin on Monday.
Hammerson would prefer to press ahead with an all-share takeover of rival Intu, which would create Britain's biggest property company with £21 billion worth of assets across Europe.
Intu operates the Trafford Centre in Manchester, while Hammerson owns the Bicester Village and Brent Cross shopping centres.
Hammerson announced at the beginning of April that severe weather and subdued consumer confidence were weighing on UK retail sales, which were down 2% in the first quarter.
However, it said that its shopping centres outperformed the market, with Bicester Village delivering a double-digit increase in the period.
The group also flagged a £3.5m hit to net rental income from the wave of retail restructurings and administrations that have afflicted the sector, including Toys R Us and New Look.