Democratic Party's presidential nominee Joe Biden praised his Indian-American running mate Kamala Harris during his nomination acceptance speech, describing the California senator as a "powerful voice" in the US and said, "Kamala's story is the American story."

Kamala Harris, 55, scripted history in US politics as she became the first Indian-American and Black woman to get a major party's vice-presidential nomination on the third day of the virtual Democratic National Convention on Wednesday.

"It will be the work of the next president to restore the promise of America to everyone. And I am not going to have to do it alone. I will have a great vice president at my side," Biden, 77, said in his acceptance speech on Thursday.

He highlighted Kamala Harris's diverse family heritage, her parents are Jamaican and Indian, and her perseverance to "overcome every obstacle she has ever faced."

"Kamala's story is the American story. She knows about all of the obstacles thrown in the way of so many in our country. Women, Black women, Black Americans, South Asian Americans, immigrants. The left out and the left behind. She has overcome every obstacle she has ever faced," he said on the last day of the four-day convention.

"No one has been tougher on big banks and the gun lobby. No one has been tougher on calling out the current administration for its extremism, its failure to follow the law, it's a failure to simply tell the truth," he said.

"Kamala and I both draw from our families. That is where we get our strength. For Kamala, it is Doug and their families. For me, it is Jill, and ours," Joe Biden said.

Introducing herself as the daughter of Indian and Jamaican immigrants at the virtual convention on Wednesday, Harris fondly remembered her Chennai-born mother who she said taught her two daughters to "be conscious and compassionate about the struggles of all people" and to believe that "the fight for justice is a shared responsibility."

"One of the most powerful voices we hear in the country today is from our young people. They're speaking to the inequity and injustice that has grown up in America. Economic injustice. Racial injustice. Environmental injustice," Joe Biden said.

"I hear their voices and if you listen, you can hear them too. And whether it's the existential threat posed by climate change, the daily fear of being gunned down in school, or the inability to get started in their first job - it will be the work of the next president to restore the promise of America to everyone," he said.

Later, Kamala Harris said in a tweet that Joe Biden will be an incredible US President.

"Tonight, Joe Biden spoke to the moment. Just like he'll do as President for our country," she tweeted.

Soon after Joe Biden concluded his speech, Kamala Harris and her husband Douglas Emhoff joined him and his wife Jill Biden.

The couples stepped onto an outside stage and embraced as they watched the fireworks light up the sky.

Before Joe Biden stepped off, reporters shouted: "How do you feel?". Biden pulled down his face mask and yelled: "Welcome to Wilmington!"

Later, in a fund-raising email and tweet, Harris said, "You're going to make an incredible President. America, we need your help to make that happen."

"As Joe Biden reminds us, character, compassion, decency - they're all on the ballot in November. Who we are and who we want to be are on the line," she said.