Dutch Prime Minister Mark Rutte has conceded he "made the wrong assessment" by not intervening against plans by the royal family to holiday in Greece.
King Willem-Alexander and Queen Maxima headed off on Friday but flew back a day later, following a public backlash.
They left as the Dutch government introduced a new partial lockdown - which included discouraging unnecessary travel - but did not break any rules.
Mr Rutte has acknowledged that he had been aware of the royal plans.
In a letter to parliament, the prime minister said he had "realised too late" that the holiday "could no longer be reconciled with the increasing infections and the stricter measures.
"This should have prompted me to reconsider the intended holiday. I bear full ministerial responsibility," he added.
The royals flew out on a government plane but were immediately criticised for going on holiday when people were being advised to stay at home as much as possible to curb the spread of Covid-19.
They flew back on a scheduled KLM flight on Saturday evening.
In a statement, the royals said: "We do not want to leave any doubts about it: in order to get the Covid-19 virus under control, it is necessary that the guidelines are followed. The debate over our holiday does not contribute to that."
Initially there appeared to be some confusion about who in government knew about the trip and whether advice had been given.
The Dutch monarchy has no formal role in the day-to-day running of the Netherlands. But the Ministry of General Affairs, headed by the prime minister, is responsible for what the monarchy says and does.
As a result, several MPs are calling on Mr Rutte to explain why he did not advise the royals to cancel their holiday.
"If Rutte had said that this was a bad idea, you can assume that the king would have changed his plans," said Peter Rehwinkel of the PvdA party.
The Green party's leader called the trip "an error in judgment" and abandoning the trip was the "only correct decision".
The daily tally of coronavirus infections continues to grow in the Netherlands. On Saturday, more than 8,000 new cases were recorded for the first time since the country's outbreak began.
Bars, restaurants and cannabis "coffee shops" have been ordered to close for four weeks.
It is not the first time the royal couple have been in the spotlight for their conduct. In August, they were pictured breaking social distancing rules with a restaurant owner during another trip to Greece.
The royal family's annual budget is under review amid growing pressure from opposition lawmakers.