U.S. Congresswoman Gabrielle Giffords remained in critical condition four days after being shot in the head in Tucson, Arizona, doctors said on Wednesday.

Doctors cautioned that Giffords still is in a dangerous phase of her recovery because of brain swelling, but they expect she will be in much better shape as early as Friday, the newspaper Arizona Republic said.

Giffords is recovering well and making small movements on her own as doctors ease sedation, indicating progress was "going as anticipated," the report quoted doctors as saying.

When asked whether she has passed the riskiest phase of her recovery, University Medical Center Trauma Director Dr. Peter Rhee said, "We're at the very edge of the woods."

Rhee said that Giffords' recovery can proceed very slowly or could "spiral downward."

"None of the downward events has occurred at this time, which is what we want," he said.

Giffords was getting "more and more responsive" as doctors reduce the sedatives administered to the gravely wounded congresswoman, Rhee said.

There likely will be permanent damage in Giffords' brain, but it is too early to gauge the extent of the damage and how it may impact prospects for her long-term recovery, Rhee said.

Other than Giffords, five patients remain in the hospital with three listed in serious condition and two in fair condition following Saturday's shooting rampage in front of a supermarket north of Tucson.

Six people were killed and 14 others wounded in the shooting that presumably targeted Giffords.

The motive for the killing remains unknown as the 22-year-old gunman Jared Loughner refused to cooperate with authorities since his arrest after the shooting.

A memorial service is scheduled in Tucson later Wednesday to remember the victims of the bloody shooting rampage.

President Barack Obama will attend the ceremony to soothe a grieving nation, the White House said.

Obama is expected to be accompanied at the memorial ceremony on the University of Arizona campus by first lady Michelle Obama, Attorney General Eric Holder and Homeland Security Secretary Janet Napolitano. Supreme Court Justice Anthony Kennedy also is attending.

"This is an opportunity for the president to heal some wounds, to send a message of cooperation and peace and really extend the olive branch to all sides," Fred Solop, chairman of Northern Arizona University's politics and international-affairs department, said in remarks published by Arizona Republic.

"This is an opportunity to define the next two years of the Obama presidency. He came off the election in a more weakened position and on the defensive. This is an opportunity to reach for the higher ground and to elevate the conversation that is taking place in Washington."