"Many people said to us: we just want to say a proper goodbye to our loved ones," the king said after meeting with around 1,000 relatives of the 193 Dutch citizens killed when the plane was shot down over rebel-held Ukraine on Thursday.
"We understand their frustration and their concern, and we share their wish for clarity about what caused this disaster," he said on television, addressing the nation for the first time.
Relatives of the deceased from around the world are becoming increasingly angry at how the disaster is being handled, with bodies stuck in a train and lax security at the crash site.
"The whole of the Netherlands feels their anger, the whole of the Netherlands feels their deep grief," said Dutch Prime Minister Mark Rutte, who also met with the bereaved relatives outside central city of Utrecht.
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"Some have lost three or four people, sometimes direct family, sometimes a friend, relative, someone from their street," Rutte said, calling on people to come together to support the bereaved.
"The thought that they've already been lying in the heat for three days, while separatists, or terrorists, I don't know what they're doing around them," Silene Frederiksz, who lost her son Bryce, 23, and his girlfriend Daisy, told De Telegraaf tabloid.
Ruud Lahaye's brother John, 54, was killed in the crash along with his partner Lilian Brouwers.
"Of course we're not happy. It's going to take six weeks before they can come back to the Netherlands," he said. "It's difficult to take on board. From here we can't do anything.