Aung San Suu Kyi, the leader of Myanmar, met Hungary's far-right nationalist prime minister Viktor Orban as part of a rare trip to Europe.
Ms Suu Kyi, who has been condemned for her handling of the Rohingya refugee crisis, held talks with the Hungarian leader in Budapest on Wednesday.
"The two leaders highlighted that one of the greatest challenges at present for both countries and their respective regions - south-east Asia and Europe - is migration," the Hungarian government said in a statement after the meeting.
"They noted that both regions have seen the emergence of the issue of co-existence with continuously growing Muslim populations."
Mr Orban said Hungary was in favour of trade co-operation between Myanmar and the EU, but rejects "attempts at the export of democracy".
The far-right leader has repeatedly clashed with the EU over the issue of immigration after his government declared "a crisis situation due to mass immigration" in 2015.
The Orban administration was accused of using anti-migrant rhetoric that fuels "xenophobic attitudes, fear and hatred" in a report by the Council of Europe's commissioner for human rights.
After his meeting with Myanmar's leader, Mr Orban said he had "great respect for Aung San Suu Kyi and all she has done for her country's freedom and democratic transformation".
Ms Suu Kyi was once lauded as a champion of democracy, but she has since fallen from grace on the world stage after failing to condemn the military's violent crackdown on the Muslim Rohingya minority in 2017.