The incident has embarrassed Prime Minister Mark Rutte's four-party coalition government, which has a precarious parliamentary majority of just one seat.
It risks undermining Dutch foreign policy at a time when diplomatic ties between the Netherlands and Russia have hit a low point, largely over the 2014 downing of Malaysia Airlines Flight MH17 over Ukraine, allegedly by pro-Russian separatists.
Zijlstra, visibly emotional as he took the floor during a parliamentary debate convened to discuss his behaviour, said he had decided to tender his resignation to the king because the situation risked harming the work of the Foreign Ministry.
"We live in a country where the truth matters. That's why I see no other option than to resign," said Zijlstra, who had held the job for less than four months. "The office (of foreign minister) must be above all doubt, both at home and abroad."
Junior Foreign Minister Sigrid Kaag, who led a United Nations mission to destroy Syria's chemical weapons in 2013-2014, will assume Zijlstra's responsibilities until a permanent replacement is found, a government official said.
Lawmakers grilled Rutte, who had previously defended Zijlstra despite having known since late January that he had not actually met Putin. They asked repeatedly why Rutte had failed to inform parliament during the three weeks before the affair went public.
Rutte acknowledged he had underestimated the impact the affair would have.
"A lie is a sin, but not a mortal sin," he said, adding that Zijlstra's remarks were accurate.
"If you look at what Russia has done in the past 10-15 years, the policy that they have followed, you must say that it's aimed at expansion," Rutte said, citing Moscow's annexation of Ukraine's Crimea region and its support for the separatists battling Kiev's forces in eastern Ukraine.
Rutte comfortably survived a no-confidence vote.
Zijlstra admitted on Monday that he had lied in 2016 when he said he had attended a meeting a decade earlier at which Putin reportedly spoke of plans for regional expansion.
He acknowledged he was not at the meeting, but insisted he had heard about Putin's remarks from a reliable source he needed to protect.
The Russian Embassy said in a statement that Zijlstra's allegations "do not hold up against any criticism and are only intended to spread false perceptions of Russia's intentions".
"Russia is being blamed for disseminating disinformation," Moscow's embassy in The Hague said in a statement.
"Dutch officials are constantly making such unfounded statements... Isn't this an example of fake news directed against our country?"
Zijlstra had been due to travel to Moscow for a previously scheduled meeting with Russian Foreign Minister Sergei Lavrov on Wednesday. That meeting was cancelled, the Russian Foreign Ministry said.
The dispute comes at an awkward time for the Dutch, who are preparing indictments against suspects in the shooting-down of MH17 over Ukraine in July 2014 with 196 Dutch citizens on board.
Dutch authorities have said the plane, flying from Amsterdam to Kuala Lumpur, was brought down by a Russian-made Buk missile, fired from territory held by pro-Russian separatists in eastern Ukraine. Russia has denied this.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.