"We're pushing on being specific on areas like Xinjiang where forced labour is taking place and where we have to express our values as a G7", the official said of the final communique to be issued at the end of the summit on Sunday.
"The atmosphere is very cooperative, it is characterized by mutual interest", Merkel said.
The multi-trillion-dollar project was launched by Chinese President Xi Jinping in 2013.
The idea of the Build Back Better World - which stemmed from a conversation between UK PM Boris Johnson and Biden - is to offer an alternative to countries so they won't have to take on incredible debt, which has happened through the BRI in the past.
With the participation of the private sector, the initiative is meant to collectively catalyze hundreds of billions of dollars of infrastructure investment for low- and middle-income countries in the coming years, the White House said.
"B3W will collectively catalyse hundreds of billions of dollars of infrastructure investment for low- and middle-income countries in the coming years", it said.
Critics say the scheme is also an instrument for extending China's diplomatic and political influence by making developing countries dependent on Beijing's largesse.
Britain also wants the world's democracies to become less reliant on the Asian economic giant.
By the end of the day, a second USA official said the countries had bridged some of their differences on the communiqué language without offering specifics.
There has been resistance from the European Union, which previous year signed a deal with Beijing giving Europe and China greater access to each other's markets.
Mr Biden believes that the West's battle for domination with China will be the defining geopolitical struggle of the 21st Century.
United States image overseas has improved with Biden election: Pew survey
Tonight it's being reported that the United States is to buy 500 million Pfizer doses to donate internationally. The president also said he will be reassuring allies about the US role in the world.
The subject also featured prominently during a brief face-to-face conversation between Prime Minister Justin Trudeau and U.S. President Joe Biden on the margins of the summit.
The U.S. came out early, telling reporters it would make a priority of singling out China's use of forced labor against the Uyghur and other minorities in Xinjiang in the text. Beijing responded with penalties on several members of the European Parliament and other Europeans critical of the Chinese Communist Party.
"While we are still finalizing the format for the meeting with President Putin and his delegation, we can confirm a few details, including the plan for both a working session and a smaller session, as well as a solo press conference by President Biden following the meeting", a White House official said. Chinese authorities have been accused of imposing forced labor, systematic forced birth control, torture and separating children from incarcerated parents.
Human-rights groups and the US and United Kingdom governments have alleged that Chinese authorities are committing genocide against ethnic Uyghurs, a Muslim minority group, and using forced labor in the northwestern Chinese region of Xinjiang.
Beijing rejects allegations that it is committing crimes.
In May, ahead of this week's meeting, the G-7 foreign leaders crafted a statement which called out China by name.
The G7 heads were also joined in person for the discussion on the coronavirus pandemic by the leaders of South Korea, South Africa and Australia. In 2019, France had invited India to attend the Biarritz Summit as a goodwill partner.
Biden ends the trip Wednesday by meeting in Geneva with Russia's Vladimir Putin.
Trudeau, left, and Biden meet virtually in February.
He added that while Trump was a "talented" and "colorful" person, Biden was a "career man" in politics, which has "some advantages, some disadvantages, but there will not be any impulse-based movements" by the US president.
"That's a different kind of person, and it is my great hope that yes, there are some advantages, some disadvantages, but there will not be any impulse-based movements, on behalf of the sitting United States president", he added.