Labor's finance spokeswoman Katy Gallagher said the comment was insensitive and hurtful to parents and children with a disability.
"As the parent of a wonderful daughter with autism, I was really upset by that comment. I found it really offensive and quite shocking," Senator Gallagher told the Seven Network.
"People who have a disability, children with autism, it is a kind of response they get all the time that people are blessed not to have what they have when in actual fact, every child is a blessing."
The comments from the prime minister show a lack of connection with everyday people, Senator Gallagher said.
"It may be a clumsy comment but they still are insensitive comments and can offend people. Maybe he can front up today and explain what he meant by that," she told Sky News.
The prime minister accused Labor of politicising his words, saying his comments were "in good faith".
"I was just simply saying that it's tough and I'm grateful that these are hardships that I and Jenny haven't had to deal with," he told 2GB.
"I was just simply trying in good faith to say: 'Look, I haven't walked in your shoes, Katherine. I'm not going to pretend to say that I understand it as well as you do'.
"Others (that) seek to leap on that and twist the words ... I thought showed really bad faith."
Liberal senator Hollie Hughes, who has a son with autism, also defended the prime minister's comments.
"I certainly didn't take anything negative away from it. I know there were days, very early on when my son was younger, that were really, really hard. I didn't feel particularly blessed," she told the ABC.
"We have a much higher suicide rate within the autism population. We have a higher unemployment rate than the general disability population. There are issues we can be angry about."
Australian of the Year and disability campaigner Dylan Alcott tweeted: "Woke up this morning feeling very blessed to be disabled - I reckon my parents are pretty happy about it too.
"Feeling sorry for us and our families doesn't help. Treating us equally, and giving us the choice and control over our own lives does."
Mr Morrison, who is campaigning in Brisbane, sought to turn the focus back to border policy, ramping up his attacks on Thursday.
The opposition leader couldn't be trusted on boat turnbacks despite Labor saying it supports the policy, Mr Morrison said.
"He can say he is going to do it, but when it mattered he didn't believe in it, he didn't do it and he opposed it," the prime minister said.
Campaign spokesman Jason Clare defended Labor's position on boat turnbacks, saying good policy should be adopted regardless of which party is in government.
"This is good practical policy development," Mr Clare said.
"You look at what works and you adopt it."
Opposition Leader Anthony Albanese, who is campaigning on the NSW south coast, sought to switch the national security debate to the coalition government failing to act on a security deal between the Solomon Islands and China.
"Where has Peter Dutton turned up? The people of the Pacific ... have all seen the video of him talking about how funny it is that countries are going to go underwater," he said.
"China is more forward-leaning. We all accept that. The difference is how do you respond to it? Do you respond to it by trying to play domestic politics? Or do you respond to it in a strategic way that makes a difference?"
Labor has even been stronger in its response to Chinese aggression, including its opposition to an extradition treaty, Mr Albanese said.
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