Ambassador of Cyprus to Cairo Khris Moritissis held a meeting with Tareq Radwan, head of the Egyptian parliament's committee on foreign relations.
A statement issued by the committee said "Radwan welcomed the visit of the Cypriot ambassador to the Egyptian parliament, affirming that bilateral relations between Cairo and Nicosia are strong and that both seek to achieve their mutual interests on the regional and international levels."
The statement added: "The Cypriot ambassador expressed concern over the Turkish escalation in the Mediterranean."
"We have concerns about this escalation, but Egypt and Cyprus have already signed a maritime boundary demarcation agreement, and this has paved the way for exploring and producing gas, and so they (Turkey) do not have any power to direct any threats to our agreement or our interests," the statement said.
For his part, Radwan told reporters that an Egyptian parliamentary delegation will visit Cyprus after the end of presidential elections next month.
"We want to reinforce relations with Cyprus at all levels," said Radwan, adding that "preparations are under way to form a joint parliamentary Egyptian-Cypriot Friendship Association."
Radwan said Turkey's objection to the Egypt-Cyprus deal is based upon the grounds that Ankara refuses to recognise the government of Cyprus.
"But as all world countries recognise the Nicosia government, Turkey will not be able to take any action against the agreement," Radwan said.
Egypt warned Turkey last week not to breach Egyptian sovereignty in the East Mediterranean region, vowing to defend its maritime borders and interests there.
Ahmed Abu Zeid, Egypt's foreign ministry spokesperson, said in a statement 7 February that Egypt would not tolerate any violation of its sovereignty and interests over the economic zone in the Eastern Mediterranean.
Abu Zeid confirmed that Cairo had ratified the Cyprus deal with several international organisations, including the United Nations.
"No party can dispute the legality of the deal, which goes in line with international law," Abu Zeid said.
Abu Zeid's warning came two days after Turkish Foreign Minister Mevult Cavusoglu said Ankara does not recognise a maritime border demarcation agreement between Cyprus and Egypt.
"We do not recognise this agreement and we plan to explore oil and gas in the Eastern Mediterranean region," Cavusoglu said.
The agreement, signed in 2003, allows both Egypt and Cyprus to explore oil and gas in their economic zones and territorial waters in the East Mediterranean region.
Italian company Eni in 2015 discovered what was considered as the eastern Mediterranean's largest gas field off Egypt's coast. The so-called "Zohr" field was officially inaugurated in January and is expected to produce 2.7 billion cubic feet of gas a day by the end of 2019.
On Sunday, a number of Egyptian MPs attacked Turkey, accusing it of funding terrorist operations in Egypt.
Independent MP Mostafa Bakri said Turkey, as the largest supporter of the banned Muslim Brotherhood organisation, is trying its best to destabilise Egypt and its economic interests.
"We got news that they are trying to impede the work of the Italian company Eni in the East Mediterranean," Bakri said, adding that "both Turkey and Qatar give a lot of support to Muslim Brotherhood-linked terrorist organisations in many Arab countries, particularly Egypt and Libya."
On Sunday, Cyprus said the Turkish military was obstructing a drill rig contracted by Italy's Eni from approaching an area to explore for natural gas.
The Saipem 12000 drill ship had been heading from a location south-southwest of Cyprus towards an area southeast of the island when it was stopped by Turkish warships on Friday, Cyprus said.