Protesters have taken to the streets of northern Greece demanding the release of two Greek soldiers detained by Turkey, amid rising tensions between the two countries.

Greece’s defence minister, Panos Kammenos, described the pair as “hostages” and ordered border patrols to be stepped up along the heavily defended land frontier the two nations share.

Sgt Dimitris Kouklatzis, 27, and Lt Angelos Mitretodis, 25, were seized 11 days ago after allegedly being found in a “forbidden military zone” deep in Turkish territory. The soldiers say they inadvertently strayed across the frontier in bad weather.

Last week a court in the Turkish border town of Edirne, where the two are being held in a high-security prison, rejected a plea for their release pending further investigation.

In rallies in Orestiada, the Greek town closest to the border, and Thessaloniki, the country’s northern capital, protesters called for the soldiers to be set free immediately.

“We want to send the message that we live in peace and harmony with our neighbours in this area,” said members of the Orestiada cycling club, who held a separate protest riding to the border in a display of solidarity for the detainees.

Kammenos said the arrests had aggravated already strained ties between the neighbouring countries. Tensions between Athens and Ankara, Nato allies but regional rivals, had reached the point where the two nations were “very close to a fatal accident”, the minister told the French daily Libération at the weekend, referring to repeated air and sea violations of Greek territory by Turkish forces.

In comments to the German newspaper Die Zeit, Turkey’s foreign minister, Mevlüt Çavuşoğlu, said the Turkish judiciary was still trying to establish whether the soldiers entered Turkey deliberately, confirming Greek fears that the pair could be charged with espionage.

“They crossed the border illegally and it is up to the prosecutors and judges who need to know what is behind this case. Did it happen inadvertently or was it deliberate? They want to be sure,” Çavuşoğlu said when asked when the men would be released.

Athens’ leftist-led government raised the case with Nato and the United Nations last week, asking both to intervene. Internationalising the case further, Kammenos told his Romanian counterpart during a visit to Bucharest that Greece was seeking support for the “immediate release of Nato, European and Greek servicemen.”

Cross-border infractions are common and Athens argues that Ankara has deliberately sought to raise the stakes in what would ordinarily be a routine affair resolved at officer level.

Suspicion has grown that the pair were deliberately snatched in a tit-for-tat move sparked by anger over Greece’s refusal to extradite eight Turkish officers who sought political asylum after a botched coup attempt against the president, Recep Tayyip Erdoğan, in July 2016.

Greece’s supreme court has rejected the extradition request, saying the eight, who remain in detention, would not be given a fair trial in a country that has become increasingly autocratic since the failed putsch.

The honorary head of the Hellenic National Defence General staff, Manoussos Paragiodakis said there was evidence to believe the two soldiers had been “set up” by a unit especially trained for the task.

“There is no way they were simply arrested by Turkish soldiers,” he told Skai TV. “It must have been some other force which is trained to do that, some kind of special force which had been trained to snatch two Greek forces. I believe the incident was set up.”

Turkish diplomats have vehemently denied the accusations. Çavuşoğlu rebuffed any suggestion that Ankara wanted to exchange the Greeks for the eight officers. “We do not want such a bargain,” he told Die Zeit.

Diplomats in Europe have become increasingly alarmed as tensions have risen markedly not only along the land border between Greece and Turkey but in the Aegean Sea and off the coast of Cyprus, where Ankara has threatened to use military force in a dispute over the ethnically divided island’s right to explore for oil and gas reserves.

In February a Turkish vessel rammed a Greek coastguard ship as both patrolled the waters off the disputes isle of Imia, causing extensive damage. In the current climate, officials fear such incidents – and the concomitant risk of an accident – is bound to increase.

The mood in Turkey has become increasingly fractious ahead of presidential and parliamentary elections next year. With the country in a state of emergency since the coup, Erdoğan and his Islamist AKP party have sought to exploit nationalist fervour, going so far as to team up with the nationalist opposition MHP party in an attempt to secure greater power.

At a rally this weekend, Erdoğan surprised supporters by making a hand gesture long associated with the fascist Grey Wolves, an unprecedented move by any leader since the foundation of modern Turkey.