The Whangārei MP is the committee's deputy chair.
He said the committee may decide to seek the views of health experts and public submissions before its recommendation was reported back to Parliament.
Dr Reti said the number of signatories to their petition was above expectation.
"We in the Health Committee have accepted petitions with way less signatures. Anything over 100 or 200 is good so I am happy that many people took part.
"Online access in parts of Northland could be challenging and combined with the fact that the petition ran for two weeks only, I think it's a good result and it shows people are concerned about this issue."
He hoped the health committee can make quick progress so ineligible pre teenagers were also protected from the deadly disease, especially during winter when meningitis peaked.
King said a lot of people were coming forward saying they could not afford the cost of vaccinating their children and the Government should act.
"Make it available for every teenager. Put people's mind at rest because we're not talking a massive amount of money here," he said.
Prime Minister Jacinda Ardern has ruled out the possibility of the Government extending free meningitis vaccines to children between 5 and 12 years in Northland for now.