It is not clear if Dutch prime minister Mark Rutte gave any advice on the holiday.
King Willem-Alexander and Queen Maxima of the Netherlands have cut short their holiday in Greece after being criticised for travelling during the coronavirus pandemic.
Though the king's vacation in Greece did not break any of the Netherlands' lockdown rules, including new restrictions introduced this week amid one of Europe's biggest coronavirus outbreaks, the government has discouraged unnecessary travel.
"This should have prompted me to reconsider the intended holiday".
"Let there be no doubt: To beat the Covid-19 virus it is necessary to follow the rules".
King Willem-Alexander and Queen Maxima flew out on a government plane and returned on a scheduled KLM flight. "The debate over our holiday does not contribute to that".
Officially, the region of Greece where the family's villa is located is under a mild Code Yellow travel warning from the Dutch Ministry of Foreign Affairs, meaning people from the Netherlands can travel, but the risk remains.
Now politicians are calling on Rutte to explain whether he advised the royal couple not to go.
Peter Rehwinkel of the PvdA party said: "If Rutte had said that this was a bad idea, you can assume that the king would have changed his plans".
The trip was an "error in judgment" and it was the "only correct decision" to call the trip off, added the GroenLinks party.
The daily tally of coronavirus infections continues to grow in the Netherlands.
The measures include bars and restaurants being ordered to close, but schools and public transport will remain open.
It is not the first time the royal couple have been in the spotlight for their conduct.
Willem-Alexander and his wife Queen Maxima issued an apology after a previous vacation to Greece, in August, after a photo was published showing them breaking social distancing guidelines on the island of Milos.
The royal family's annual budget is under review amid growing pressure from opposition lawmakers.