After an unusual private meeting at the White House on Wednesday with Mark Rutte, the Nato secretary general, Donald Trump seemed to renew his threats against the defensive military alliance for not helping fight the US-Israeli war on Iran, and hinted that he could again try to seize Greenland from Nato member Denmark.

Trump, who normally revels in conducting public meetings with visiting dignitaries on television, initially made no statement on what was discussed with Rutte, but after the former Dutch prime minister who leads the military alliance went on CNN to cast the discussion as a “frank and open” discussion “between friends”, the president issued a blistering, all-caps social media post aimed at further unsettling Nato.

“NATO WASN’T THERE WHEN WE NEEDED THEM, AND THEY WON’T BE THERE IF WE NEED THEM AGAIN. REMEMBER GREENLAND, THAT BIG, POORLY RUN, PIECE OF ICE!!!” the president wrote in a manner that did little to dispel concerns that he might try to withdraw from the military alliance.

Rutte, who has drawn criticism in Europe for seeming to endorse Trump’s decision to launch a war of choice against Iran without consulting Nato allies, and then scolding them for not helping to deal with its consequences, told CNN that “some” Nato members had failed in their response to Trump’s angry demand that they take part in the war on Iran by forcing open the strait of Hormuz.

After no Nato country responded to Trump’s demand for help, he announced that the US did not want or need any such help.

“I really admire his leadership,” Rutte also said of Trump, while refusing to say whether he left the meeting reassured that the US would remain in Nato, or alarmed that Trump might try to withdraw from it.

Asked if he believed NATO countries were tested and failed, Rutte said: “Some of them yes, but a large majority of European countries, and that’s what we discussed today, have done what they promised before in a case like this.”

Earlier on Wednesday, Trump’s press secretary, Karoline Leavitt, told reporters that withdrawing from Nato is something the president “has discussed” and would likely raise with the secretary general.

Before his meeting with Trump, a jovial Rutte posed with the US secretary of state, Marco Rubio, at the state department.

While Trump has spoken as if he has the power to pull the US out of Nato, a 2023 law, co-sponsored by then senator Rubio, requires Senate approval, or an act of Congress before a president can suspend, terminate or withdraw US membership in Nato.

At the time, Rubio said the law would “ensure that current and future U.S. Presidents cannot leave NATO without rigorous debate and consideration by the U.S. Congress with the input of the American people”.