Arizona Rep. Gabrielle Giffords announced on her website Sunday that she will resign from Congress this week to continue her recuperation from the brain injury she suffered when shot last January.

“A lot has happened over the past year. We cannot change that,” Giffords, 41, says in a video on her website, speaking in a halting manner.

“I don’t remember much from that horrible day, but I will never forget the trust you placed in me to be your voice,” Giffords continues. “Thank you for your prayers and for giving me time to recover. I have more work to do on my recovery. So to do what is best for Arizona, I will step down this week.”

Giffords, a Democrat, will submit a letter of resignation during the week to House Speaker John Boehner and Arizona Gov. Jan Brewer. Brewer said Sunday in a statement that she will call a “special primary and general election” to fill the state’s 8th congressional district seat for the rest of Giffords’ term, which expires at the end of the year.

A statement from her office said Giffords will attend the State of the Union address Tuesday as one of her last acts before stepping down.

She also will finish her “Congress On Your Corner” event that was interrupted by the shooting rampage of Jan. 8, 2011, that killed six people and wounded 13 others, including Giffords, the statement said.

President Barack Obama was effusive in his praise for the congresswoman, saying Giffords “embodies the very best of what public service should be.” He added that her “cheerful presence will be missed in Washington (and) she will remain an inspiration to all whose lives she touched — myself included.”

“Over the last year, Gabby and her husband Mark have taught us the true meaning of hope in the face of despair, determination in the face of terrible odds, and now — even after she’s come so far — Gabby shows us what it means to be selfless as well,” Obama said in a statement.

Boehner, an Ohio Republican, said that Giffords “will be missed.” And Brewer, the Arizona governor, lauded Giffords as a “noble public servant … and a model of what can be accomplished with persistence and determination.”

House Democratic leader Rep. Nancy Pelosi, D-Calif., called Giffords a “bright star” whose “message of bipartisanship and civility is one that all in Washington and the nation should honor and emulate.”

“Her legacy in the Congress and her leadership for our nation will certainly continue,” Pelosi said in a statement.

In her website video posted Sunday, Giffords says her public service career has not ended.

“I will return, and we will work together for Arizona and this great country,” she says.

Earlier this month, Giffords joined thousands for a vigil in Tucson, one of several emotional events over the weekend to mark one year since the shootings.

Prosecutors accuse Jared Lee Loughner, 23, of carrying out the attack, which purportedly targeted Giffords during the constituent meet-and-greet event outside a supermarket.

Giffords is still recovering from her injuries, and her right side remains weak. She has made few public appearances since the incident with some rare exceptions, such as casting a vote in Congress to raise the federal debt ceiling and conducting an interview with ABC’s Diane Sawyer.

She has been undergoing intensive rehabilitation in Houston, but returned to Tucson several times, according to her office.

Pia Carusone, the congresswoman’s chief of staff, said recently that Giffords had steadily increased her workload as her condition improved.

“As the year wore on, we were able to plug the congresswoman in more,” Carusone said. “Now we talk regularly over video chats and telephone. She’s gotten more and more involved the better she gets.”

Rep. Debbie Wasserman Schultz of Florida, the Democratic National Committee chair, said that Giffords — a close friend — came to the conclusion that going back to her job this year would reduce the time and work she could put into her recovery.

Giffords’ return to Tucson for the one-year anniversary of the shooting showed her “how challenging it would be. It came into focus then,” Wasserman Schultz said.

“Gabby doesn’t do anything halfway,” she said. The most important thing for Giffords was to continue her recovery, which is “more likely to be years, not months,” she continued.

Loughner potentially faces the death penalty if convicted on charges of murdering six people — including the chief federal judge of Arizona, John Roll. Loughner has been diagnosed as schizophrenic and has spent time on suicide watch while in custody and is undergoing treatment in Springfield, Mo.

A federal appeals court in May cleared the way for him to be forcibly medicated over the objections of Loughner and his attorney.

Giffords herself worked at PricewaterhouseCoopers and as CEO of El Campo Tire, her family’s business, before being elected to the Arizona House of Representatives in 2000. Two years later, she became the youngest woman elected to the Arizona state senate.

She won a November 2006 election to earn her spot in the U.S. Congress, then captured two other terms.

A flood of people posted comments on Giffords’ Facebook page Sunday under her video — praising the congresswoman for her courage, voicing their continued support and expressing hope that she’ll one day return to public office.

One person wrote, “I am so thankful you are taking care of you. We can wait.”

Another commenter called Giffords an “inspiration” and a “great example.”

“It’s so sad to see you leave but I know we’ll see you back soon. Be well. You are loved,” he wrote.

— CNN’s Tom Cohen and Dana Bash contributed to this report.