President Emmanuel Macron has told Boris Johnson to “get serious” or remain locked out of discussions over how to curb the flow of people escaping war and poverty across the Channel.

In a further sign of an escalating diplomatic crisis since the deaths of 27 people on Wednesday, the French leader criticised the UK’s decision to issue a five-point plan via Twitter instead of conducting bilateral talks.

The letter to Macron was sent publicly as a tweet in time for the front pages of UK newspapers.

“I spoke two days ago with Prime Minister Johnson in a serious way,” Macron said at a press conference on Friday. “For my part I continue to do that, as I do with all countries and all leaders. I am surprised by methods when they are not serious.

“We do not communicate from one leader to another on these issues by tweets and letters that we make public. We are not whistleblowers. Come on. Come on,” he said.

His words followed the French government’s decision on Friday to withdraw an invitation to the home secretary, Priti Patel, to attend a meeting on the issue.

The French interior minister, Gérald Darmanin, wrote to Patel to say the meeting on Sunday would proceed without British involvement.

Darmanin told Patel the letter from Johnson to Macron, suggesting France take back people who cross the Channel, was a “disappointment”.

Referring to Johnson’s posting of the letter on social media, he added: “Making it public made it even worse. I therefore need to cancel our meeting in Calais on Sunday.”

The French government’s official spokesperson, Gabriel Attal, added to criticism of Johnson’s letter on French television, calling it “mediocre in terms of the content, and wholly inappropriate as regards the form”.

Attal told BFM TV the letter was “mediocre because it does not respect all the work that has been done by our coastguards, police, gendarmes and lifeboat crews … It basically proposes a ‘relocation’ agreement, which is clearly not what’s needed to solve this problem.

“We’re sick and tired of this double talk and outsourcing of problems.”

Attal continued: “What we need is for the British to send immigration officers to France to examine here, on French territory, demands for asylum in Britain.”

He added that the tone of the letter “did not in the least reflect the exchanges Emmanuel Macron had with Boris Johnson … It’s as if Boris Johnson was regretting leaving Europe, because as soon as he has a problem he considers that it is Europe’s responsibility to solve it. It doesn’t work like that – it works through cooperation.”

France was planning to host ministers from all states with Channel coasts, including Patel, for a meeting on the refugee crisis in Calais on Sunday.

A source close to Darmanin told Agence France-Presse and French media the meeting would be going ahead with the ministers from other European countries but said Patel was no longer invited after Johnson’s “unacceptable” letter.

“We consider the British prime minister’s public letter to be unacceptable and contrary to the discussions we had with our counterparts,” said the source, who asked not to be named.

“Therefore, Priti Patel is no longer invited to the inter-ministerial meeting on Sunday, which is maintained in the format of France, Belgium, the Netherlands, Germany and the European Commission.”

Grant Shapps, the transport secretary, dismissed suggestions that Johnson’s letter was sent to generate headlines and insisted it was made in good faith. “I can assure our French friends of that and I hope they will reconsider,” he told Radio 4’s Today programme.

Johnson wrote to Macron asking France to immediately start taking back all migrants who land in England after crossing the Channel.

Taking people back “would significantly reduce – if not stop – the crossings, saving thousands of lives by fundamentally breaking the business model of the criminal gangs” behind the trafficking, he said.

Johnson’s letter also set out areas for greater cooperation with France, proposing joint border patrols, aerial surveillance and intelligence sharing.

The new row adds to the post-Brexit tensions between Britain and France, with French fishers on Friday due to stage a blockade of Channel ferry ports and stop freight entering the Channel tunnel in protest at fishing rights.

In a further development, the head of a UK trade union that represents thousands of Border Force staff has warned members could be balloted to strike if they are asked to push back boats of people.

Patel claimed in parliament on Thursday that Border Force was ready and prepared to turn around boats that have come from France and send them back.

The PCS general secretary, Mark Serwotka, said: “It is shocking that the government is suggesting Border Force staff turn boats back, which will clearly be against international law and morally reprehensible.

“PCS is reviewing all its options, including taking out a judicial review against Priti Patel’s plans and a possible industrial response.”