As the opposition, advocates, and some coalition MPs push for the sick to be brought here, the former prime minister said health services were better there than in some parts of regional Australia.
"We'll continue to work progressively on that, but we're not going to do it by showboating and grandstanding", the prime minister told reporters in Geelong.
Mr Abbott says people on Nauru are "very well looked after" despite a leading Australian paediatricians warning children could die if they are not taken elsewhere.
As pressure mounts on the Morrison government to remove children and their families from Nauru, Tony Abbott insists "it's no hell hole" and is actually a "pleasant island".
Mr Morrison said about 30 people had been taken off Nauru over the past few weeks.
"Of course "Kids Off Nauru" is a great slogan but it's a awful guide for policy", he told 2GB.
"We trust you have been engaging already with the New Zealand government on arrangements to move vulnerable asylum seekers as soon as it becomes possible to do so".
Nauru is an island paradise, according to Mr Abbott.
HBO Boxing: Jacobs vs. Derevyanchenko Results
Sergey Derevyanchenko, in particular, noted that it is not aims to fight Jacobs, but if he has the opportunity he will seize it. According to CompuBox statistics, Jacobs landed 181 of his 578 overall punches, 21 more than Derevyanchenko (160 of 658).
Independent MP Cathy McGowan believes Mr Abbott is in the minority, saying the tide of public opinion has turned in favour of getting asylum seeker children off Nauru.
Eleven children were evacuated earlier this week, leaving 52 on the island.
"If you like living in the tropics, it's a very, very, pleasant island".
"There's willingness now to not only get the kids off, but I hope the next step is to stop indefinite detention", she told ABC radio on Monday.
Labor has said it will "seriously consider" resettling asylum seekers from Nauru to New Zealand, but is critical of proposed laws banning those refugees from ever coming to Australia.
There is overwhelming support from the Australian public for the Australian government to accept New Zealand offer's to resettle refugees now in detention on Nauru.
Both the coalition and Labor do not support a bill before parliament to bring detainees to Australia for urgent medical care, but the Greens would do what it could with crossbench support, he added.