Gibbs apologized if anyone was "unduly" alarmed but did not elaborate.
"Jake, I'm telling you what he meant to say," he said to laughter.
Department of Homeland Security Secretary Janet Napolitano earlier today also tried to temper the vice president's remarks.
"I think the vice president, if he had, if he could say that over again he would say if they're feeling sick they should stay off public transit or confined spaces because that is indeed the advice that we're giving," Napolitano said on MSNBC.
Sen. Tom Harkin, D-Iowa, who said Biden's comments were unfortunate, was visibly frustrated by what he called misinformation.
"I wish the vice president had checked with the Centers for Disease Control ... before he made that statement. ... As far as not riding on subways or planes, we're not going to shut down our system and that doesn't get to the nub of the problem, anyway," he said on Radio Iowa. "So I think that's very unfortunate that this kind of misinformation got out."
House Speaker Nancy Pelosi, D-Calif., also had a different message. She said she would not tell her family to stay off planes and public transportation, but would recommend to them the "common-sense" approach, washing hands and covering sneezes or coughs.
"They are living their lives and, again, practicing common sense, good practices. And so it's not a question of not encouraging, not to travel. It's also a question of encouraging them not to leave home ... just because their states ... are the most, shall we say, suspicious in this case," Pelosi told reporters.
Biden's spokeswoman, Elizabeth Alexander, released a statement shortly after the vice president's remarks, saying, "The advice he is giving family members is the same advice the administration is giving to all Americans: that they should avoid unnecessary air travel to and from Mexico. If they are sick, they should avoid airplanes and other confined public spaces, such as subways. This is the advice the vice president has given family members who are traveling by commercial airline this week."
The CDC has confirmed 131 cases of swine flu in 18 states. The World Health Organization has tallied 236 cases globally, most of them in Mexico.
The CDC recommends against any non-essential travel to Mexico, but it has not said to avoid travel altogether because of flu concerns. The U.S.-Mexico border remains open, and airlines have not canceled flights.
At a news conference on the 100-day anniversary of his administration, President Obama reiterated the need for individual responsibility in staying safe from the flu but advised against panic.
"This is a cause for deep concern but not panic," he said. " If you are sick, stay home. If your child is sick, keep them out of school. If you are feeling certain flu symptoms, don't get on an airplane. Don't get on any system of public transportation where you're confined and you could potentially spread the virus."
He said his advisers did not believe the U.S.-Mexico border should be closed. "From their perspective, it would be akin to closing the barn door after the horses are out, because we already have cases here in the United States," he said.
Biden also said this morning that doing so would be a "massive undertaking" and that no benefit would come from it.
The House Energy and Commerce Health Subcommittee convened today the fourth congressional hearing this week on swine flu with CDC and Health and Human Services officials. Napolitano will hold a briefing Thursday afternoon.
ABC News' Jake Tapper, Dean Norland, Karen Travers and David Chalian contributed to this report.