Gore, campaigning at a child-care center in New York, also proposed tax breaks to help parents pay for day care or to keep their kids at home.
His plan would cost about $8 billion over the next decade for the incentives for states, aides said.
Interviewed on ABC's Good Morning America, Gore said most working parents use some type of child care and much of it is inadequate.
"In a lot of states there are just no standards, there's not even a criminal background check to see if abusers are hired, there's no training, there's a very high turnover with low wages for these people, and the job they're doing is critical," Gore said.
"We require hundreds of hours (of training) for people who take care of hair but no training for people who take care of children, and that ought to change," he said.
Gore's child-care proposals could appeal in particular to women, whose support had seemed to be softening in the spring. A Voter.com/Battleground poll last month showed that since March, when Republican George W. Bush clinched the GOP nomination, the Texan had turned a 5-point deficit among women into a 4-point lead.
As part of his push to better prepare children to enter school, Gore said his plan would require participating states to establish early-reading programs and would give bonuses to staff that complete literacy training.
Some 13 million children under age 6 are receiving child care in the United States, but only 14 percent of centers have been rated as high quality, a Gore aide said.
Gore was also asked about Russia's reluctance, restated during President Clinton's visit to Moscow, to agree to modifying the Anti-Ballistic Missile Treaty to allow the United States to move toward even a limited anti-missile system.
Asked whether he might be prepared, if elected president, to pull out of the treaty, Gore said, "I wouldn't rule that out."
But, he added, there is a big difference between "tearing up the treaty and throwing it away" and what he proposes: "a modest, affordable and limited system that's designed to protect us against one of these rogue states that might have a handful of weapons, five, 10, 15 years from now."
Gore's position is consistent with the Clinton administration's and he has said before that he would consider abandoning the treaty if the United States was seriously threatened by a missile attack from a rogue nation.
He said on Monday that he believes Russia will eventually agree to modify the treaty to allow the U.S. to build a limited system.
The money for Gore's child-care plan would come from the projected federal budget surplus. The Department of Health and Human Serices would have to approve a state's plan before it could receive federal dollars.
As part of Gore's effort to make child care more affordable, he promises that if elected president he would expand the child care tax credit to cover half the cost - up to $2,400 - and make it available to those families whose incomes are so low that they pay no tax. Currently, the credit is not available to such families and covers only 30 percent of child care costs for families that are eligible.
Child care costs average about $63 per week, or $3,376 per year, according to the 1990 National Child Care Survey. Child-care workers are paid an average of $5.08 per hour, according to a 1993 study.
Gore also proposes to give tax relief to parents who stay home with their children. He would allow parents of children younger than a year to claim assumed child-care expenses of $500.