Sebelius has until Thursday to deal with the measure. She has a strong record of supporting abortion rights.
The measure is described by anti-abortion members as an attempt to strengthen enforcement of existing restrictions on late-term procedures. Critics say the bill is really an attempt to restrict access to abortion.
Sebelius spokeswoman Beth Martino said the governor is reviewing the bill thoroughly.
The bill imposes more detailed reporting requirements on doctors who perform late-term abortions. Also, if a woman or girl came to believe her late-term abortion was illegal, then she, her husband or parents could sue the doctor for damages.