The Turkish president, Recep Tayyip Erdoğan, on Saturday warned his French counterpart, Emmanuel Macron, “not to mess” with Turkey, as tensions between the Nato allies escalated.

“Don’t mess with the Turkish people. Don’t mess with Turkey,” Erdoğan said during a televised speech in Istanbul on the 40th anniversary of the 1980 military coup.

Macron has strongly condemned Ankara during a standoff between Greece and Cyprus on one side and Turkey on the other over hydrocarbon resources and naval influence in the eastern Mediterranean.

Erdoğan urged Greece to “stay away from wrong” actions in the disputed waters backed by countries such as France, which stepped up its military presence in the region after rival naval exercises by Athens and Ankara last month.

The US has urged Turkey to cease activities that are raising tensions in the eastern Mediterranean, with secretary of state Mike Pompeo calling on all sides to back diplomacy.

“We remain deeply concerned by Turkey’s ongoing operations surveying for natural resources in areas over which Greece and Cyprus assert jurisdiction over the eastern Mediterranean,” Pompeo told reporters during a visit to Cyprus on Saturday, in which he met Republic of Cyprus president Nicos Anastasiades and foreign minister Nikos Christodoulides.

“Increased military tensions help no one but adversaries who would like to see division in transatlantic unity,” he added. “Countries in the region need to resolve disagreements, including on security and energy resource and maritime issues diplomatically and peacefully.”

Pompeo said his trip to Cyprus would complement phone calls by Donald Trump with his Turkish counterpart Erdoğan and Greek prime pinister Kyriakos Mitsotakis.

Macron on Thursday had said Europeans must be “clear and firm with, not Turkey as a nation and people, but with the government of President Erdoğan, which has taken unacceptable actions”.

The French leader was speaking before the summit of the EU’s seven Mediterranean nations, which threatened Turkey with sanctions over its activities.

The latest tensions began after Turkey deployed the Oruc Reis research vessel and warships to the disputed waters on 10 August and prolonged the mission three times.

But the Turkish leader on Saturday dismissed such remarks and accused Macron of “lacking historical knowledge”.

“Mr Macron, you’re going to have more problems with me,” Erdoğan threatened.

They were his first comments directly taking aim at the French leader after remaining silent during the latest row.

He also said France “couldn’t give a lesson in humanity” to Turkey, and told Macron to look first at France’s own record, notably in Algeria and its role in the 1994 Rwandan genocide.

Demonstrating the ire Macron’s comments have raised, Erdoğan on Saturday evening again took aim at the French leader.

“Macron, you already don’t have much time. You’re on your last legs,” Erdoğan said during a speech in Istanbul as part of a campaign to sign up new members to his ruling party.

The next French presidential election will be in 2022.

Relations between Turkey and France have deteriorated over the eastern Mediterranean, but the two allies disagree on other major issues including the Syria and Libya conflicts.

Ankara and Paris have previously traded barbs after French officials in 2018 met Syrian Kurdish leaders linked to a US-backed militia viewed by Turkey as terrorists.

The two countries are also on opposing sides in Libya, where Ankara backed the UN-recognised Government of National Accord in Tripoli against a 2019 offensive by military leader Khalifa Haftar.

France is suspected of supporting Haftar, but insists it is neutral in the conflict.

Erdoğan accused France in his first speech on Saturday of intervening in Libya “for petrol”, and in Africa for “diamonds, gold, copper”.

Cypriot president Anastasiades welcomed Pompeo’s comments as evidence of the US’ “firm stance on condemning Turkey’s illegal drillings within (Cyprus’) exclusive economic zone”.

Pompeo’s “visit at a time when crucial developments are taking place in the eastern Mediterranean, due to Turkey’s illegal actions, aptly demonstrates the sincere concern and interest of the US in preserving stability in our region,” he said.

Turkey’s “unlawful activities … should be immediately terminated,” he said, adding however that he conveyed Cyprus’ support for resolving disputes in the eastern Mediterranean through dialogue.