Labour claims Prime Minister David Cameron has "serious questions to answer" about the government's approach to the plight of Christians facing persecution in Iraq.
Shadow foreign secretary Douglas Alexander said the UK's failure to follow France and Germany in offering them asylum will "no doubt raise grave concerns."
He added: "The UK government rightly took steps to help avert humanitarian catastrophe in Iraq and Labour has welcomed decisions to now offer support to the Kurdistan regional government and assist Kurdish forces with technical and logistical military equipment.
"But alongside steps to support the Kurdish forces, the UK must now work to engage regional partners to help build a more inclusive and stable government in Iraq.
"That regional approach must focus on supporting and stabilising Jordan, which now shares a border with the ISIS-held areas, as well as bringing countries like Turkey into efforts to secure regional stabilisation."
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A cloudy and wet start on Saturday across many central and southern areas of the UK.