Lord Alton asked about the UK government's response, including "what consideration they have given to the case for referring the government of Burma to the International Criminal Court?"
According to the United Nations (UN), renewed fighting between the Myanmar Army and Kachin Independence Army has led to the displacement of at least 4,000 civilians since early April.
In a statement on 9th June, to mark the seventh anniversary of the resumption of conflict in Kachin State, Global Kachin Communities claimed as many as 7,000 have been displaced in the past two months.
In his response, Lord Ahmad of Wimbledon, Minister of State at the Foreign and Commonwealth Office (FCO), expressed the government's "deep concern" at the situation.
"We have called upon the Burmese military and all parties to cease hostilities and allow the humanitarian access that is required to be provided to displaced people.
"Turning to Rakhine, the Burmese authorities must show that the commission of inquiry can deliver accountability for the perpetrators of atrocities. If not, the Government will consider supporting international routes to justice," he said.
Rt Rev Alan Smith, Lord Bishop of St Albans noted that "the reported atrocities against the Rohingya have been described as crimes against humanity, ethnic cleansing and genocide", and asked "whether the human rights violations in Kachin and Shan states meet the criteria of at least crimes against humanity and war crimes?"
Lord Ahmad agreed that ethnic cleansing has taken place against both people groups "but because of the lack of access for international agencies it is difficult to determine the issue of genocide".
He added that there is hope for Myanmar because the UN has now gained access to parts of country for the first time.
"We will continue to impress on both the civilian and military authorities for that access to be applicable universally across the country," he said.
Religious freedom charity Christian Solidarity Worldwide (CSW) has welcomed the debate and said the world needs to pay attention.
Benedict Rogers, CSW's East Asia team leader: "Seven years after the Burma Army broke a ceasefire with the Kachin Independence Army (KIA), the humanitarian consequences of this conflict are very grave and the human rights violations continue to be perpetrated with impunity.
"The world has, understandably, focused on the terrible suffering of the Rohingyas, but it is essential that the Kachin and others in northern Burma are not forgotten, and that urgent steps are taken to end this conflict, bring about a genuine, meaningful and inclusive peace process through political dialogue, ensure unrestricted access for humanitarian aid to reach those displaced by war, and address impunity."
On 26th April, the UN announced the appointment of Christine Schraner Burgener of Switzerland, an experienced diplomat, as his new Special Envoy on Myanmar.
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