Gamid Shabanov and Mehman Agamemdov were each told on Monday to pay £665 after police broke up the gathering of 30 people in the southern village of Aliabad.
UK Minister of State for Foreign and Commonwealth Affairs, Sir Alan Duncan said: "We regularly raise human rights issues with Azerbaijan, including freedom of religious belief."
Sir Alan was responding on Tuesday to a written question put to him by the Democratic Unionist Party MP, Mr Gregory Campbell.
Mr Campbell asked the minister: "If he will hold discussions with the Azerbaijan authorities on recent reports of the persecution, arrest and fining of Christians in that country."
Sir Alan went on to say: "Most recently, on 5th December, I discussed human rights in a meeting with the Ambassador of Azerbaijan.
"The British Embassy in Baku engages with officials from the State Committee Working with Religious Associations and we regularly meet representatives of religious communities in both Azerbaijan and the UK to discuss religious freedom."
Some members of the Christian community in Aliabad, southern Azerbaijan.
Holding religious meetings in private homes has been outlawed in Azerbaijan - a country located between Russia and Iran in the Caucasus region - and only registered organisations can hold prayer meetings.