The EU is warning Greece it faces suspension from the Schengen passport-free travel zone unless it overhauls its response to the migration crisis by mid-December, as frustration mounts over Athens’ reluctance to accept outside support.

Several European ministers and senior EU officials see the threat of pushing out Greece over “serious deficiencies” in border control as the only means left to persuade Alexis Tsipras, Greece’s prime minister, to deliver on his promises and take up EU offers of help.

If the EU follows through on its threat, it would mark the first time a country has been suspended since passport-free travel was established in the Schengen Agreement of 1985.The challenge to Athens comes amid a bigger rethink on tightening joint border control to ensure the survival of the Schengen zone. The European Commission will this month propose a joint border force empowered to take charge of frontiers, potentially even against the will of frontline states such as Greece.

Greece’s relatively weak administration has been overwhelmed by more than 700,000 migrants crossing its borders this year. Given the severity of the crisis, EU officials are vexed by Athens’s refusal to call in a special mission from Frontex, the EU border agency; its unwillingness to accept EU humanitarian aid; and its failure to revamp its system for registering refugees.

EU home affairs ministers, who meet on Friday, are to make clear that more drastic measures will be considered if Greece fails to take action before a summit of EU leaders in mid-December, according to four senior European diplomats. The suspension warning has been delivered repeatedly to Greece this week, including through a visit to Athens by Jean Asselborn, foreign minister of Luxembourg, which holds the EU’s rotating presidency.

One Greek official strongly denied accusations that Athens has been unco-operative and said claims Mr Tsipras has failed to meet pledges made at a summit of western Balkan leaders last month were “untrue”.

But another official acknowledged the foot-dragging. He said it stemmed from a legal requirement that only Greeks were allowed to patrol the country’s borders as well as sensitivity over the long-running dispute over Macedonia’s name and suspicions about Turkish designs on certain Greek islands, including Lesbos, point of entry for many migrants.

As Greece shares no land borders with Schengen, Greek officials point out the country’s suspension from the passport-free area will have no impact on migrant flows. “There are no refugees leaving Greece who are flying,” he said. EU officials acknowledge this but say the withdrawal of travel rights for Greeks is one of their few points of leverage over Mr Tsipras.

Athens has recently turned down a deployment of up to 400 Frontex staff to immediately reinforce its border with Macedonia, complaining in a letter to the European Commission that their mandate was too broad and went beyond registration.

Greek officials have yet to accept an invitation to invoke an emergency aid scheme — the EU civil protection mechanism — that would rush humanitarian support to islands and border areas.

In spite of months of encouragement from the EU, it has declined to call in Frontex’s rapid intervention team, as it did in 2011 to help on its land border with Bulgaria. Greece showed more openness over invoking this so-called “rabit” mechanism during Mr Asselborn’s visit, according to officials familiar with the talks.

EU diplomats complain that Greece has also not fulfilled its promise to arrange three flights to relocate migrants to other member states. Partly due to problems of registration in Greece, just 159 of the planned 160,000 refugees have been relocated within Europe.

A third Greek official insisted the fraught talks with the EU would be resolved within the fortnight. “It was tough,” he said of the negotiations. “They are very demanding, some member states are very demanding.”

The disputes have prompted the commission to take the unusual step of backing Macedonia’s decision to erect a fence with Greece. A spokesperson said the former Yugoslav republic had “the right to take the measures it finds necessary” to better manage the flow of migrants from Greece, which still runs at several thousand a day.

Eastern European leaders have been Greece’s most vocal critics. On Sunday Robert Fico, the prime minister of Slovakia, said “it is high time” to evict Greece from Schengen, adding that all member states were privately in agreement on the issue. “We cannot tolerate one of the member countries openly refusing to fulfil its obligations to protect the Schengen borders,” said Mr Fico. “In such a situation, the Schengen area is useless.”

Berlin has so far resisted calling for Greece to be suspended or expelled. But behind the scenes, frustrations are growing in Austria and Germany, who have both considered sending special envoys to Greece to support the migration efforts, according to one official familiar with the plans.

“The red line for the Germans was not allowing Frontex to come in and help them,” said one EU ambassador in Brussels. “The Germans are furious and that’s why people are talking about pushing Greece out.”

Two EU ambassadors said debates over Greece were becoming increasingly heated, with Luxembourg, which holds the rotating chair of the EU council of member states, warning Greece that “other measures” may be taken unless it makes good on its promises.

Some Greek analysts suspect Athen’s foot-dragging on border controls may be partly about trying to win concessions on implementation of its third bailout: softer terms on tough measures such as pension cuts and farmers’ taxes, for example, and postponements of unpopular structural reforms.

Aris Hatzis, an Athens university professor and political commentator, says: “Tsipras saw the refugee issue as a bargaining chip but it’s going to backfire disastrously if the threat of Schengen suspension becomes a public issue.”

The Commission will deliver an oral update on Greece’s situation to a meeting of EU home affairs ministers on Friday, followed by a written assessment to a summit of EU leaders in mid-December.

If serious shortcomings are still evident, Athens has been warned that EU leaders may request the commission start suspension proceedings, triggering a review of Greece’s borders that can take three months.