Mr Biden laid a wreath at a solemn service held in steady rain in Washington DC, where a moment of silence was held to mark the exact time a hijacked plane hit the Pentagon at 9.37am.
“Twenty-one years, and we still kept our promise to never forget,” Mr Biden said as he recognised the impact the 2001 attacks had on the US and the world and honoured the nearly 3,000 people killed that day.
“For all those of you who lost someone, 21 years is both a lifetime and no time at all. It’s good to remember, the memories help us heal, but they can also open up the hurt and take us back to that moment when the grief was so raw.”
Recalling the day, Mr Biden said that “terror struck us on that brilliant blue morning”.
“The American story itself changed that day,” he said.
“But what we cannot change, never will, is the character of this nation that the terrorists thought they could wound.”
Mr Biden also spoke of US efforts to track down al-Qaida leadership and the drone strike that killed Ayman al-Zawahiri in Afghanistan in early August.
“It took 10 years to hunt down and kill Osama Bin Laden, but we did.
“And this summer I authirorised a strike on Zawahiri… because we will not rest, we’ll never forget, we’ll never give up. Now Zawahiri can never threaten the American people.”
Mr Biden quoted the late Queen Elizabeth II, who sent a message to the US people after the 2001 attacks to say: “Grief is the price we pay for love.”
The president used the address to appeal for the kind of national unity seen in the aftermath of the nation’s darkest day.
“I hope we’ll remember that amidst those dark days, we dug deep, we cared for each other, and we came together,” Mr Biden.
Americans remembered 9/11 on Sunday with readings of victims’ names and tolling bells 21 years after the deadliest terror attack on US soil.
There were moments of silence held at 8.46am and 9.03am at Ground Zero in New York, to mark the time that hijacked planes crashed into the north and south towers of the World Trade Centre.
Vice president Kamala Harris and her husband Doug Emhoff attended the ceremony, held at the National September 11 Memorial Museum in New York where the towers formerly stood.
First lady Jill Biden was attending a service at the Flight 93 National Memorial Observance in Shanksville, Pennsylvania with victims’ relatives and dignitaries.
Speaking on CNN, Hillary Clinton warned that the US must remain vigilant against extremism “of any kind”.
“We have … been reminded about how important it is to try to deal with extremism of any kind, especially when it uses violence to achieve political and ideological goals,” Ms Clinton told State of the Union host Dana Bash.
Some Americans joined in volunteer projects on a day that is federally recognised as both Patriot Day and a National Day of Service and Remembrance.
Sunday’s ceremonies came a year after the US made its chaotic final withdrawal from Afghanistan, effectively bringing to an end the so-called war on terror that it launched in response to the attacks.