Catherine, the Princess of Wales, announced on Monday that she had completed chemotherapy for her cancer, lifting a cloud from the British royal family after an anguished period in which she and her father-in-law, King Charles III, had both been stricken with serious illness.

Speaking in an emotional three-minute video, Catherine said, “As the summer comes to an end, I can’t tell you what a relief it is to have finally completed my chemotherapy treatment.”

“Doing what I can to stay cancer-free is now my focus,” she continued. “Although I have finished chemotherapy, my path to healing and full recovery is long, and I must continue to take each day as it comes.”

The videotaped announcement was highly personal, offering home-movie-style glimpses of Catherine with her husband, Prince William, and their three children. But it left many questions unanswered: whether her doctors have declared her medically free of cancer, whether she is still undergoing other forms of treatment and her prognosis for a full recovery.

Kensington Palace did not indicate that Catherine was cancer-free. And officials did not offer further details on the princess’s medical condition, citing her right to privacy. It has never confirmed what type of cancer she was being treated for, how far the disease had progressed or the details of her treatment, beyond chemotherapy.

Dr. Claudine Isaacs, an oncologist and professor of medicine at the Lombardi Comprehensive Cancer Center at Georgetown University, said that, in general, doctors were cautious about declaring a patient free of cancer because there could be microscopic cancerous material that escaped detection.

“Often, we can’t detect any cancer,” Dr. Isaacs said, “but that does not guarantee the person is, or will remain, cancer-free.”

Catherine said she looked forward to returning to work and would undertake a limited schedule of public events for the rest of the year. She is expected to attend a ceremony honoring those killed in war at the Cenotaph monument in November, one of the most somber dates on the royal calendar.

“The last nine months have been incredibly tough for us as a family,” Catherine said. “Life as you know it can change in an instant, and we have had to find a way to navigate the stormy waters and road unknown.”

The announcement, filmed last month by Will Warr, a London videographer who specializes in wedding videos, put the emphasis on recovery and family rather than clinical details. Shot in gauzy light with a mix of soft focus and newsreel-style images, the video showed Catherine playing with her children, resting her head on William’s shoulder and walking through a field of waving grain.

Catherine, 42, spoke in a voice-over about her ordeal, which began after Christmas, when she entered a hospital for abdominal surgery.

“The cancer journey is complex, scary and unpredictable for everyone, especially those closest to you,” Catherine said. “With humility, it also brings you face to face with your own vulnerabilities in a way you have never considered before, and with that, a new perspective on everything.”

Over footage of her son Prince Louis scampering up a pile of logs, the family laughing during a card game around a kitchen table with Catherine’s parents, frolicking on the beach and walking hand in hand through forest and fields, Catherine characterized her illness as having pulled her focus back to the things that matter.

“This time has above all reminded William and me to reflect and be grateful for the simple yet important things in life, which so many of us often take for granted,” Catherine said. “Of simply loving and being loved.”

Charles, who announced in February that he, too, had been diagnosed with cancer, has returned to public duties, though Buckingham Palace has not yet said whether he continues to undergo treatment. His wife, Queen Camilla, offered the closest thing to a health update last week when she said of her husband, during a visit to a cancer center in Bath, “He’s doing very well.”

Catherine’s tentative return to public life began in June when she attended Trooping the Color, a military parade that honors the birthday of the king. She rode in a state carriage to watch the parade with her children, Prince George, Princess Charlotte and Louis.

Hopes for Catherine’s condition rose when she made a second public appearance in July, on the final day of the Wimbledon tennis tournament. Wearing a royal purple dress, she won an enthusiastic standing ovation from spectators, including the actor Tom Cruise, as she entered the gallery. Later, in her role as the royal patron of the All England Lawn Tennis and Croquet Club, Catherine presented the Challenge Cup to the men’s singles champion, Carlos Alcaraz of Spain.

Still, Catherine has tried to manage public expectations about her recovery since she spent 14 days in a hospital and announced the cancer diagnosis in March.

“I am making good progress,” she said in a statement issued the day before she took part in the birthday parade, “but as anyone going through chemotherapy will know, there are good days and bad days.”

“On those bad days you feel weak, tired and you have to give in to your body resting,” Catherine added. “But on the good days, when you feel stronger, you want to make the most of feeling well.”

Kensington Palace, where Catherine and William have their offices, has pleaded with the news media to respect her privacy, following weeks of breathless rumors about her condition earlier in the year. There has been relatively little speculation since she announced her diagnosis in a stark, prerecorded video.

As she has at other key phases of her recovery, Catherine has sought to keep tight control over how she discloses information to the public. Mr. Warr, the filmmaker who shot the latest video, also produced a video for the couple on their 10th wedding anniversary. In addition to wedding videos, Mr. Warr works for commercial clients like Puma, Red Bull and Tesco, according to his LinkedIn page.

Palace officials said the video was meant to underscore how the natural world has been a sanctuary for Catherine during her recovery. In her therapeutic language, she sought to make her ordeal a source of hope for others.

“To all those who are continuing their own cancer journey,” she concluded, “I remain with you, side by side, hand in hand. Out of darkness can come light, so let that light shine bright.”