"It's the most extraordinary case of recovery I've ever seen in a human being," the actor said in an interview with The Associated Press.
Reeve came to fame as the "Man of Steel" in four Superman films made from 1978 to 1987.
Since his accident, he has established a foundation that gives grants to paralysis sufferers and helps fund spinal-injury research.
Reeve, 50, who requires round-the clock care and breathes with the help of a respirator, has consistently expressed hope he will walk again.
"I don't take kindly to ultimatums," he said Wednesday. "I think doctors should be very careful before they tell a patient, 'You only have a year to live' or 'You'll never walk again.'"
Research into spinal injuries, he said, "is moving by leaps and bounds … Old barriers are falling on a regular basis."
Five years after his accident, Reeve surprised doctors by regaining some movement in his right wrist, left fingers and both legs.
In March, he underwent surgery to have electrodes implanted in his diaphragm, a procedure that allows him to breathe for periods without a respirator.
He said he was encouraged by research at the Weizmann Institute into macrophages – "scavenger cells" that can help cleanse the site of an injury, allowing healing to begin.
Israel also is a major center for stem cell research, which many scientists believe could be used to treat a vast array of conditions, from spinal injury to diabetes and Parkinson's disease.
However, stem cell research has been restricted in some countries because obtaining the cells involves destroying a human embryo. U.S. federal law prohibits government funding of research that results in the death of an embryo, and Reeve has been critical of the U.S. stance.
"I think the United States is not leading the world in the area of stem cell research, and it could be, and in my opinion it should be," Reeve said.
Israel has no law regulating embryonic stem cell research.
Reeve, who arrived in Israel Monday for a five-day trip, has visited research institutions and facilities for the disabled.
On Wednesday, he met President Moshe Katsav and visited Jerusalem's Western Wall and the Yad Vashem Holocaust memorial.
Reeve's visit is a rarity for a country many international celebrities have avoided during almost three years of violence.
Reeve said people around the world are "holding our breaths and hoping there'll be peace after so many centuries of conflict."
At a visit to Jerusalem's Alyn hospital, which treats disabled children and adolescents, Reeve met Rahab Badar, 24, a Druse woman from northern Israel who fractured her neck when she was hit by a car seven years ago.
She was told she would never walk again, but now can – after years of therapy – walk with the aid of a walker.
"It's a miracle I can walk," she said. "Hopefully one day Superman, with God's help, will be able to walk as well."
