The group, Midwives and Nurses For Life, says that if women opt for a surgical termination, nurses and midwives will be asked to provide the pre- and post-operative care, which they object to.
The petition states they find the "end of life of a foetus is morally objectionable", and that "participation includes any supervision, delegation, planning or supporting of staff involved in termination of pregnancy".
The group states that although the new proposed legislation provides for freedom on conscience, it states the staff involved must refer the patient on to another staff member, which they see as participation in the procedure.
Mary Fitzgibbon, a nurse, midwife and lecturer; Fiona McHugh, a paediatric nurse; and registered nurse Margaret McGovern spoke to the media about what they see as lack of negotiation from the government with those "who will be at the coalface" when legislation is implemented.
"We want to be sensitive to the women, I don't want to meet a woman in the morning and later tell her I'm not getting involved in her care.
"We need to have that discussion at ward level, with our nurse managers, but that is not happening," Ms Fitzgibbon said.
"There's a lot of anxiety, a lot of fear, people are worried about promotional aspects if they say they're invoking freedom of conscience, where does that leave them?"
The petition, which has been live for over two weeks on social media, is a culmination of 367 registered nurses and midwives, according to the Nursing and Midwifery Board Ireland (NMBI) there are over 65,000 registered staff currently practising in Ireland.
"As with any change, there has to be discussion, we just feel that we've been ignored during the whole process because we have repeatedly asked how this is going to work in practice in an already overstretched healthcare service," Ms McHugh added.
Speaking on Tuesday, they said they had made repeated attempts to contact Health Minister Simon Harris to no reply.
They have also tabled amendments to the new legislation, which includes providing pain relief to the foetus during terminations, which they compared to animal welfare in veterinary practice and "dignified disposal" of remains.
A spokeswoman for the Department of Health said: "Section 23 of the Health (Regulation of Termination of Pregnancy) Bill 2018 covers conscientious objection.
"It states that where he/she has a conscientious objection, a medical practitioner, nurse or midwife shall not be obliged to carry out, or to participate in carrying out, a termination of pregnancy."
Simon Harris has said abortion services should be in place by the new year.
In May, the Irish electorate voted overwhelmingly in favour of removing a controversial amendment of the constitution, which gave equal right to life to the unborn and the woman, and allowing terminations up to 12 weeks of pregnancy without restriction.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
