Prostatitis: This condition, particularly chronic prostatitis, can cause pain in the lower abdomen that radiates to the rectum due to the proximity of the prostate gland to the rectum. The pain is often accompanied by urinary symptoms.

Diverticulitis: Inflammation of a diverticulum in the colon can cause lower abdominal pain that may radiate to the rectum, especially if the affected diverticulum is in the sigmoid colon.
Irritable Bowel Syndrome (IBS): While IBS can present with a variety of symptoms, some patients experience abdominal pain that can radiate to the rectum, along with changes in bowel habits.
Hemorrhoids: Large hemorrhoids can cause pain, especially if they are thrombosed, and this pain can be perceived as radiating to the rectum.

Appendicitis: Although appendicitis typically presents with pain that initially is diffuse or around the navel and then localizes to the right lower quadrant, atypical presentations can occur, especially if the appendix is retrocecal, potentially causing pain to radiate to the rectum.
Ectopic Pregnancy: A pregnancy that develops outside the uterus can cause severe abdominal pain that may radiate in various directions, including to the rectum, especially if the ectopic pregnancy is in the lower pelvic area.
Intestinal Obstruction: Obstruction of the intestines can cause severe abdominal pain that may radiate to the rectum, along with nausea, vomiting, and changes in bowel habits.

Rectal Cancer: While rectal cancer can cause pain, it is less common for the pain to be the primary symptom. However, advanced rectal cancer can cause pain that radiates to the lower abdomen.
Pudendal Neuralgia: This is a rare condition characterized by pain in the distribution of the pudendal nerve, which can include the rectal area, but it is less likely to cause abdominal pain.
Coccydynia: Pain in the coccyx (tailbone) can radiate to the rectum but is typically associated with trauma to the area or prolonged sitting.