Biden, speaking at a U.S.-Africa Leaders Summit event, said the United States is looking to increase collaboration in all areas.
"Africa belongs to the table in every room - in every room - where global challenges are being discussed, and in every institution where discussions are taking place," Biden said.
"It's been a long time in coming, but it's gonna come."
South Africa is currently the only G20 member from Africa. The AU is made up of 55 member states.
Biden's remarks, and the summit, aim to position the United States as a partner to African countries amid competition with China, which has sought to expand its influence there by funding infrastructure projects on the continent and elsewhere.
Chinese trade with Africa is about four times that of the United States, and Beijing has become an important creditor by offering cheaper loans - often with opaque terms and collateral requirements - than Western lenders.
African leaders largely welcomed the summit. But the continent has also been reluctant to take sides among major powers.
African Union chair Moussa Faki Mahamat deplored that the years since the Cold War have seen "waves of national selfishness" on the international stage.
Senegalese President Macky Sall, the current chair of the African Union, welcomed U.S. support for the institution and voiced appreciation for Biden's summit.
But he also called for the U.S. to end longstanding rights sanctions on Zimbabwe and voiced alarm over a bill in Congress that would impose sanctions on African countries over dealings with Russia.
"This would be the first time in international relations that a whole continent is targeted," Sall said.
African leaders from 49 countries and the AU have gathered this week in Washington for a three-day summit that began on Tuesday.
The summit is the first of its kind since one in 2014 under former U.S. President Barack Obama.
To kick it off, the Biden administration pledged $55 billion for food security, climate change, trade partnerships and other issues. Biden later announced an additional $15 billion in funding for Africa.
This report includes some information from Agence France-Presse.