Biden, who now oversees a foreign policy center at the University of Pennsylvania and domestic policy center at the University of Delaware, said he was "disgusted and appalled" by reports that "authorities in the Russian republic of Chechnya have rounded up, tortured, and even murdered individuals who are believed to be gay."
"I hope that the current administration lives up to the promises it has made to advance human rights for everyone by raising this issue directly with Russia's leaders," Biden said. "The United States must lead the way to demand an end to these egregious violations of human rights."
Human rights groups and media in the Russian republic have reported an increasing number of reports of gay men disappearing. Some have reported being detained, while the fate of others remains unknown.
Novaya Gazeta, the newspaper that broke the story, reported earlier this month that more than 100 gay men had been detained and three have been murdered.
CNN has not confirmed the reports, but human rights groups have substantiated aspects of reporting from the predominantly Muslim republic inside Russia.
Biden, who led the way inside the Obama administration when it came to speaking out about same-sex marriage, said in the statement that "every man or woman on this earth is entitled to be treated with dignity -- to live without fear and to love freely."
The United Nations office on human rights has also condemned the reports.
"It is crucial that reports of abductions, unlawful detentions, torture, beatings and killings of men perceived to be gay or bisexual are investigated thoroughly," a statement posted on the website for the Office of the United Nations High Commissioner for Human Rights said.
Tensions with Russia have been high of late, making it unlikely that the Trump administration's calls would be heard in Russia.
Trump told reporters this week that relations between the United States and Russia are at an "all-time low."
A White House spokesperson did not respond to questions about Biden's call for Trump to act.