The discussions concern Ukrainian men between the ages of 23 and 60.
"This is also what Ukrainians are asking us to do," Brunner said, commenting on discussions about potentially ending temporary protection for Ukrainian men.
Nicolas Ioannides, Cyprus' deputy minister for migration and the representative of the country currently holding the rotating presidency of the Council of the European Union, said all EU member states agree that the Temporary Protection Directive for Ukrainians should be extended until March 2028.
However, he said many countries support "changes to the scope of protection under certain conditions."
The European Commission is expected to present a proposal in the coming weeks on the future of temporary protection for Ukrainian refugees.
On June 1, Euractiv reported that European countries were considering excluding military-age men who had left Ukraine unlawfully from an extended temporary protection program.
On June 2, Corinna Ullrich, a representative of the European Commission's Directorate-General for Migration and Home Affairs, confirmed that such discussions were taking place. She added that any restrictions would not apply to Ukrainians already covered by temporary protection, including more than 1.15 million Ukrainian male refugees currently living in the EU.
A decision on extending temporary protection for Ukrainian refugees could be made in July or September 2026.