It also said it would have a "minimal equity impact" compared with other cancers, such as lung cancer, where the inequities for Māori and Pacific were higher.
Deputy director-general for population health and prevention Deborah Woodley has confirmed the age would not be lowered.
Hawera bowel cancer patient Archie Hurunui said that was not good enough.
"I think it's a weak excuse - they spend money on a number of other things that we don't get to see, so the evidence out there at the moment is that our health system is not that great and we need to contribute more money into it."
He said while 50 was a "good place to start", he wanted it to be dropped even further to 35.
"You can't label [that] you're going to get colon cancer at this particular age because you don't know until you actually do that investigative stuff and you find out things aren't happening too well with your body, then all of a sudden you're going, 'oh no you've got cancer'.
"Don't automatically think people at a particular age are the ones who're going to get it because some of the people I've met are well and truly under that age so how do you help those people who are in that particular age group and then can't access the medicines that are available out there."
Whanganui woman Esther Tinirau has had bowel cancer for four years and doesn't know how much time she has left.
"That's not something I am keen to know, but we'll just take each step as it comes - I've just been through six months of chemotherapy as well as an unfunded drug Cetuximab that I had to fund myself and with good results, so basically I am in remission - for now," Tinirau said.
She was just 51 when she was diagnosed with bowel cancer, although she'd been having symptoms for 18 months prior.
She had to fight her GP to get tested, and said a screening programme would have meant the disease was caught much sooner.
"For the Government to come out and say that they won't lower the age for bowel screening is really disappointing because Māori feature highly in that and we're twice as more likely to die from bowel cancer than non-Māori so it's a pretty disappointing announcement for me, having contracted the disease when I was 51."
National Māori Cancer Leadership Group Hei Āhuru Mōwai chairwoman Dr Nina Scott said that to get rid of the equity gap the age range for Māori and Pacific must be dropped.
"Māori get bowel cancer younger but also, the impacts of bowel screening are going to be much, much higher for the New Zealand European group and that means that we're going to grow the equity gap."
She was also concerned that Māori leaders were not being listened to.
She said a national screening pilot programme run between 2012 and 2017 screened Māori from age 50, so she didn't understand why it couldn't be done now.
"The arguments keep going around and around about why that can't happen and the rational keeps changing so I think fundamentally, people just don't want it to happen."
Trainee doctor and communications lead at Hapai te Hauora, Emma Espiner, said the ministry was "hiding behind the capacity issue".
"They're saying they can't do equity at the moment, but I just don't think that really washes and I'm suspicious the announcement is happening now during an election where people say you can't really have these conversations around the election because they get polarised," Espiner said.
Woodley said the priority was to get Māori and Pasifika people screened for bowel cancer (58 per cent and 44 per cent respectively) above the national target of 60 per cent.
"Whilst we acknowledge the need to extend the age range to increase health gains for Māori and Pacific peoples, our review of resourcing implications supports the view that the only viable and safe option is to introduce the change once the programme is fully rolled out," she said.
The ministry would consider lowering the age once the current screening programme was completely rolled out, which is expected to be by December 2021.
