Cross bench peer Lord Alton submitted nine written questions to Parliament on the subject of Pakistani Christians and their plight.
He is concerned that not enough is being done to support believers who live in the predominantly Muslim country.
It is thought tens of thousands of Pakistani Christians have already fled violence to countries such as Thailand and Sri Lanka, where tourism visas are relatively cheap.
Lord Bates answered one of the questions saying: "The UK recognises there may be individual cases of religious persecution.
"However, not all Christians are at risk.
"It is important to carefully consider each case on its merits."
Lord Alton recently returned from a visit to Thailand to examine the lives of asylum seekers living in detention centres in the country.
The head of the British Pakistani Christian Association, Wilson Chowdhry, had told Premier he's not impressed with the responses given. He said: "These answers reveal that the UK government says it does not itself know the number of Pakistani Christians who have fled to Thailand, Malaysia and Sri Lanka through fear of persecution, but, according to the FCO, they continually press the Pakistani government to meet international law obligations, including those relating to religious minorities in Pakistan."
Lord Alton has told Premier that he's "seeking a meeting" with the government concerning these answers.
One question asked to the government discussed opportunities for exploitation and trafficking of these refugees: "what assessment they have made of the risks of those Pakistani refugees who are living without legal status while their asylum claims are being assessed in Bangkok falling victim to trafficking and exploitation."
Baroness Anelay of St Johns answered - stating that because Thailand is not a signatory to the 1951 UN Convention on refugees and therefore have no legal status in the country.
"Once any form of legal immigration status expires they are then deemed to be illegally in the country.
"Many are detained in Immigration Detention Centres awaiting deportation, or resettlement by the UNHCR should they qualify.
"Others live a vulnerable life as urban refugees open to trafficking and exploitation."
She added that they are continuing to work closely with the UNHCR in Thailand on a wide range of refugee issues.
Commenting on the answers that Lord Alton received to these written questions, Wilson Chowdhry told Premier that: "Pakistani Christians seeking resettlement as refugees in Thailand have to endure absolutely horrific conditions, they live in a climate of profound fear, and there have been numerous preventable deaths because of their inability to access work or medical treatment and care.
"We understand in some cases it is taking as long as a decade to get resettled, which is not acceptable.
"We call on the FCO and UNHCR to redouble efforts in this regard, noting in particular that given the long timescales and that most are apparently getting refugee status, the lack of education means that these Christians are being denied the opportunity to contribute to the host society and economy as much as they could, and we urge the Thai government to move quickly to change this situation, because the short term costs would be outweighed by the long term benefits.
"These Pakistani Christian refugees have among them a high proportion of doctors, lawyers, teachers and other professionals who would be eager to contribute to Thai society and economy, but they can't do that if they are forced to scrap for illegal work, and their children will not be able to do so as effectively as they could otherwise do if they continue to be denied educational opportunities as they are now."
You can access the petition here.
Listen to Premier's Marcus Jones speak to Wilson Chowdhry on Premier's News Hour here: