The government has approved a draft law to end women's right to have the procedure on demand up to 14 weeks of pregnancy, but the text has not yet gone to parliament for a vote amid dissent within Rajoy's Popular Party.
"We are not going to withdraw the law," Rajoy vowed on Tuesday in an interview on Spanish radio station Cadena Ser.
The draft reform, approved in January, would allow abortion only in cases of rape reported to the police or a medically-certified threat to the mother's physical or psychological health.
"This is a difficult subject. We have presented a draft bill and are prepared to talk and debate it with anyone who wants to," Rajoy said.
"It was in our election manifesto and we are ready to listen to everyone and to try to produce something reasonable."
The former Socialist government brought Spain into line with much of Europe when it passed the current law in 2010.
Existing legislation allows women to opt for abortion in the first 14 weeks of pregnancy, and up to 22 weeks if the foetus is seriously deformed or if the birth poses a serious risk to the mother.
The planned reform has outraged pro-choice groups and brought thousands of people out onto the streets to protest.