As deputy leader, Davis is filling in for Prime Minister Jacinda Ardern in Labour's caucus while Peters will take over as Acting Prime Minister when Ardern goes to hospital to have her baby.
Peters, who is also Foreign Minister, said Davis was entitled to a view on the matter but he did not intend to weigh in beyond saying New Zealand would not undertake such an policy itself.
"With the greatest respect, I could have views on every other country in the world. We are trying to run this country. I'm not going to spend the next six weeks of this important time focusing on every other country but my own."
In the past six weeks about 2000 children have been split from their parents at the US border under a "zero tolerance" approach which sees adults detained to face charges while children were placed into centres run by the Office of Refugee Resettlement because they could not be jailed.
National leader Simon Bridges said the practice was "highly regrettable" and "inhumane."
"When you've got even the President's wife and former First Lady Laura Bush coming out against that, you can certainly see why as mothers. Separating families in this way seems inhumane."
Melania Trump criticised the practice, saying through a spokesperson last week she "hated to see children separated from their families" and both Republicans and Democrats should agree on immigration reform.
"She believes we need to be a country that follows all laws, but also a country that governs with heart," the spokesperson said.
Former First Lady Laura Bush has also criticised it as "immoral" and "wrong."
Under former US President Barack Obama families had been detained as a group but the courts ruled they could not be detained indefinitely so the practice changed to releasing families until their cases were heard.