The Morrison government has quietly transferred several refugee families to Australia from Nauru this week amid mounting internal pressure to get children off the island after five years.

But the Coalition has made little attempt to garner Senate support for a piece of legislation Prime Minister Scott Morrison says is a prerequisite to sending 150 refugees to New Zealand.

Meanwhile, the chief medical officer for the contractor hired to look after refugees' health on Nauru was "stood down" from her post for "breaking the rules", and deported on Wednesday.

Prime Minister Scott Morrison said decisions on medical transfers were made on a case-by-case basis. Credit:Alex Ellinghausen

Fairfax Media understands the government enacted this week's medical transfers in the wake of previous Federal Court decisions ordering severely ill refugees be sent to Australia.