"Collectively, we're giving Parliament, the Government and Pharmac the strong message that there needs to be significant change and it must happen now.
"New Zealanders are suffering and dying without vital medicines and the Government can't continue to ignore this."
Burgess said there needed to be an independent review of Pharmac's model, which she said hadn't changed for 25 years.
"Decision processes are slow, non-transparent and closed to input by those affected and in many cases the clinical experts who understand the value of medicines," she said.
The health select committee recently voted against holding its own review of Pharmac, which was the subject of an earlier petition. The committee's chairwoman, Labour MP Louisa Wall, said an independent review would be more appropriate.
The committee is also currently considering petitions calling for two breast cancer drugs, Kadcyla and Ibrance, to be funded by Pharmac. Some women with advanced breast cancer are raising the $6000 they need each a month for treatment themselves.
Those who cannot fundraise miss out. Pharmac is waiting for a recommendation by its expert oncology committee before making a decision on funding. That is expected shortly.
A spokesman for Health Minister David Clark said a decision would be made today on whether he would meet the petitioners on Parliament's forecourt.
Labour MP Kieran McAnulty, along with National MPs Simon O'Connor and Paula Bennett, ACT leader David Seymour, NZ First MP Jenny Marcroft and Greens co-leader Marama Davidson will accept the petitions.
Last week Bennett accepted a petition calling for Pharmac to fund Spinraza, a $1 million drug to treat Spinal Muscular Atrophy.
An application has been made to Pharmac, which is awaiting the outcome of two clinical trials.
The eight petitions being presented today are for:
Breast cancer
Chronic lymphocytic leukaemia
Lung cancer
Lung cancer – non-small-cell lung cancer
Myeloma
Multiple myeloma
Ovarian cancer
Pompe disease