Last month, Mrs May accused judges of making the UK more dangerous by ignoring rules aimed at deporting more foreign criminals and said they were choosing to "ignore parliament's wishes".
Asked about the criticisms, Lord Neuberger replied: "I think attacking judges is not a sensible way to proceed. It causes me concern but it does not alarm me. No government has done anything to undermine judges. It is unfortunate that the Home Secretary has acted and spoken as she has done."