Police department spokesman Lt. Fabian Pacheco said an officer checking Giffords' office in Tucson found "a real strange" device that he described as a medal container resembling a coffee can and with writing on it. Pacheco would not disclose what the writing said.
He said authorities warned people at a candle light vigil across the street from Gifford's office that they may hear loud noise as a bomb squad worked to render the device safe, but they should not be alarmed.
Pacheco said there was no threat to public safety.
"It's been a horrible and tragic day," he said. "The prudent thing for us is to take everything seriously."
Giffords was holding a forum for constituents earlier Saturday when the violence erupted, killing six and wounding several others, including Giffords.
At the candle light vigil held, more than 100 people huddled in the cold, held candles and read signs that said "Peace," and "Just Pray."
"She's just a great person," said Margaret Robles, 64, a retired teacher's aid who knew Gifford's grandparents. "She didn't care what color, what race, if you could read or if you were a scholar. She treated you as an equal."
Pima County Sheriff Clarence Dupnik gave few other details about the possible package.
