US authorities had originally denied access to schoolchildren from a number of Muslim-majority nations to participate in the science competition, decisions that followed implementation of stricter visa policies under President Donald Trump.
But following public outcry over the Afghan girls' inability to attend the event, the US president urged US authorities to reverse course, according to US media.
"I am most grateful to the US Government and its State Department for ensuring Afghanistan, as well as Gambia, would be able to join us for this international competition this year," said the president of the First Global organization, Joe Sestak, who noted that teams from Yemen, Libya and Morocco would also attend.
"All 163 teams from 157 countries have gained approval to the United States, including Iran, Sudan, and a team of Syrian refugees," said Sestak, a former US Navy Admiral and congressman.
"I could not be more proud."
The six girls from Herat, Afghanistan reportedly were blocked from attending the robotics competition even after two rounds of interviews for a one-week visa.
The visa rejections appeared to contradict the administration's claim that it wants to empower women globally.
When the reversal was announced, Trump adviser and daughter Ivanka Trump tweeted: "I look forward to welcoming this brilliant team of Afghan girls, and their competitors, to Washington DC next week!"
The July 16-18 competition aims to build interest and confidence in engineering and technology in schools worldwide.
Meanwhile in March, every single African due to attend the African Global Economic and Development Summit, a trade conference in California, had their visa request rejected, according to organisers.
A limited version of Trump's travel ban -- termporarily visitors from Iran, Libya, Somalia, Sudan, Syria and Yem -- recently took effect, after the US Supreme Court allowed it to be enforced pending a full hearing in October.
Travelers from Afghanistan and The Gambia are unaffected by that measure.
