Uncertainty over how Britain's referendum on June 23 on whether to stay in the European Union will play out has prompted investors to buy Danish crowns, seen as a safe haven.
That has helped strengthen the currency to the upper end of the tight band to the euro the central bank has kept it within.
The central bank intervened in the currency market in May for the first time in three months, buying foreign reserves and selling its own currency, which helped ease pressure on the crown towards the end of the month.
The Nationalbank is ready for unlimited intervention and to let its reserve of foreign exchange "sky rocket", central bank governor Lars Rohde told a press meeting on Wednesday.
He said the bank could also cut interest rates further, a stronger tool used less often than foreign exchange intervention to weaken the crown. In January the bank raised its certificate of deposit rate to minus 0.65 percent from minus 0.75 percent.
"We did not (reach) the lowest possible rate last year, so there is the possibility to go further into negative territory if needed," Rohde said.
Last year, speculators poured money into the AAA-rated country's currency, betting Denmark would drop the three-decade-old currency peg and let the crown rise, after the Swiss National Bank scrapped its cap on the franc against the euro.
At 1108 GMT, the crown was trading at 7.4357 per euro <EURDKK=D3>.
Under the ERM2 Exchange Rate Mechanism, the crown must stay within 2.25 percent of a rate of 7.46038 per euro. In reality the central bank has kept to a much tighter range of plus/minus 0.50 percent.
(Additional reporting by Erik Matzen and Jacob Gronholt-Pedersen,; editing by John Stonestreet)
By Teis Jensen