A week after saying that his family may lack the "emotional fuel" for a White House bid, Vice President Joe Biden on Thursday again fueled speculations that he may jump into the race after all, CNN reported.

"If I can reach that conclusion that we can do it in a fashion that would still make it viable, I would not hesitate to do it," Biden told the crowd at the Ahavath Achim Synagogue in Atlanta. "The most relevant factor in my decision is whether my family and I have the emotional energy to run. The honest-to-God answer is: I just don't know."

The vice president earlier this year lost his oldest son, Beau, a former Army officer and attorney general of Delaware who had been diagnosed with brain cancer in 2010. In a May 30 conference call with members of the Democratic National Committee, Biden had described his family as "in deep grief," the New York Times noted.

But the 72-year-old former senator has never explicitly ruled out a presidential bid, though many observers doubt that he could mount a successful challenge to Democratic front-runner Hillary Clinton at this stage of the process, according to Politico.

"I can't imagine him undertaking such a monumental underdog effort at such a difficult time for his family and with the massive monetary, people and campaign advantages of the Clinton campaign," an unidentified heavyweight from the crucial primary state of New Hampshire said last week.

But Biden has been deliberating a potential bid in private and consulted with advisers, including popular Massachusetts Sen. Elizabeth Warren, who herself has repeatedly ruled out a presidential campaign.

"Unless I can go to my party and the American people and say that I'm able to devote my whole heart and my whole soul to this endeavor, it would not be appropriate," he said on Thursday. "The other people in the race and whether I can raise the money and whether I can get an organization; that's not the factor. The factor is: Can I do it? Can my family?"