Instead, she said, she'll leave it to Biden to decide -- amid "the grief and the heartbreak" of the death of his son, Beau -- whether to run.
"I just want the vice president to decide to do what's right for him and his family," Clinton told reporters Wednesday after a campaign event in Ankeny, Iowa, calling Biden a "friend."
Speculation about a Biden run has taken off in recent days as Clinton has continued to be dogged by her use of a personal email address on a private server during her tenure as secretary of state. Biden's aides and allies have discussed how he might mount a campaign, and the vice president has taken meetings -- both with top Democratic operatives and with Massachusetts Sen. Elizabeth Warren, a progressive icon.
Clinton said she understands Biden faces a "really hard" decision.
Beau Biden, a rising political star in Delaware, reportedly urged his father to run for president before dying of brain cancer earlier this year.
The vice president has been tending to family responsibilities in recent months, but has begun setting meetings to figure out how he might mount a late entry into the field.
Biden sat down with two top President Barack Obama hands, former communications director Anita Dunn and long-time lawyer Bob Bauer, and has scheduled more meetings. He also got Obama's "blessing" to run in a private meeting -- though it's not clear whether Obama would endorse him.
Clinton called Biden a friend, noting that the two were Senate colleagues, where Clinton represented New York and Biden represented Delaware, and in Obama's cabinet, where Clinton was the first-term secretary of state.
She said she has "a great deal of admiration and affection for him, and I think he has to make what is a very difficult decision for himself and his family. And he should have the space and the opportunity to decide what he wants to do."
In a softer tone than usual, Clinton also noted that she attended Beau Biden's funeral.
"I mean, I cannot even imagine the grief and the heartbreak. I mean Joe has had more terrible events than most people can even, you know, contemplate. Losing his first wife, losing his first daughter, now losing his son," Clinton said. "He has to do what he has to do. But I'm just going to continue with my campaign."
Clinton was flanked Wednesday by former Iowa Gov. Tom Vilsack, another Obama administration veteran as agriculture secretary, who has endorsed her candidacy.
Vilsack echoed Clinton's praise for the vice president, saying: "I love Joe Biden, just like we all do. He's a wonderful man."
"They call them campaigns for a reason," Vilsack said. "They're tough. They're hard. Choices are difficult."