The proposed bipartisan legislation comes at a time when soaring underage use of e-cigarettes has health experts alarmed, the Associated Press reported.
McConnell's home state of Kentucky was long one of leading tobacco producers in the country, but he said passage of the bill is "one of my highest priorities."
"Kentucky farmers don't want their children to get hooked on tobacco products while they're in middle school or high school any more than any parents anywhere want that to happen," McConnell said on the Senate floor, the AP reported.
The bill was co-sponsored by Sen. Tim Kaine, D-Va., another state that's been a major tobacco producer.
Fourteen states have enacted laws raising the minimum age for tobacco sales to 21, according to the anti-smoking Campaign for Tobacco-Free Kids. Similar action has been taken by 470 municipalities, the AP reported.
A recent federal government survey found that 1 in 5 U.S. high school students reported using e-cigarettes the previous month. Most e-cigarettes contain highly addictive nicotine, which can harm young people's brain development and may increase their risk of smoking cigarettes later in life, according to the U.S. Centers for Disease Control and Prevention.
"Youth vaping is a public health crisis," McConnell said Monday. "It's our responsibility as parents and public servants to do everything we can to keep these harmful products out of high schools and out of youth culture."
The American Cancer Society's advocacy organization, the Cancer Action Network, said the bill is a "welcome indication that Congress is taking the alarming crisis of increased youth tobacco use seriously and is committed to taking action," the AP reported.
But it warned against including amendments that could override stronger restrictions by states and municipalities, exempt some young people or exclude certain products.