"We can and we will get it under 6 percent," Biden said in the nationally televised debate at Centre College in Danville, Ky. He did not say when a new Obama administration would lower the rate from the current 7.8 percent.
Ryan, a Wisconsin congressman and Republican presidential nominee Mitt Romney's running mate, said lowering the unemployment rate to 6 percent was the "entire premise" of the Romney campaign's economic plans.
Biden also said the next president would likely nominate one or two new U.S. Supreme Court justices and said Romney's choices would endanger the legality of abortion.
Biden, a Roman Catholic like Ryan, said he personally accepts the church's opposition to abortion rights, but "I just refuse to impose it on others, unlike my friend here, the congressman."
Ryan -- when asked, like Biden, to explain his views about abortion in personal terms -- recalled an early ultrasound of his first child when he saw the heartbeat. He then said he opposed abortion except in cases of rape or incest.
In a discussion about the White House's 2009 economic stimulus package, Ryan assailed the program as ineffective, prompting Biden to say Ryan had written to him twice to request stimulus funding for his state.
"We advocated for constituents who were applying for grants," Ryan responded. "We do that for all constituents."
"I love that," Biden replied. "This is such a bad program, and he writes me a letter saying ... we need this stimulus" because it creates jobs.
The debate opened with Ryan and Biden clashing over the Sept. 11 attack at the U.S. consulate in Benghazi, Libya, that killed U.S. Ambassador Christopher Stevens and three other Americans.
Ryan accused the administration of failing to provide proper diplomatic security in Libya and said the administration's foreign policy in general "projects weakness."
Biden defended the administration's response in Libya, saying officials based shifting public statements about the attack on intelligence assessments available at the time.
He also said Republicans in Congress cut $300 million from diplomatic security.