Ersin Tatar said he reiterated the necessity of acceptance of equal international status during a meeting with UN Secretary-General Antonio Guterres.
Tatar told reporters following his return from Brussels that he had a "beneficial" and "sincere" meeting with Guterres.
He said Guterres will evaluate if there will be a second 5+1 meeting in Geneva after meetings in New York in September.
"It is out of the question for us to go directly to official negotiations," he added.
The unofficial first 5+1 meeting -- with both sides of the island, guarantor countries Turkey, Greece and the UK, and the UN – was held in Geneva from April 27 – 29 but no common ground was found to begin the negotiations process.
Guterres suggested that the process "could be accelerated and handled more seriously" with the appointment of a special representative for the process, said Tatar, adding his country will consider the suggestion.
The island of Cyprus has been divided since 1974 when a Greek Cypriot coup aimed at Greece’s annexation of the island was followed by violence against the island’s Turks and Ankara’s intervention as a guarantor power.
It has seen an on-and-off peace process in recent years, including a failed 2017 initiative in Switzerland under the auspices of the guarantor countries.