South Africa's National Prosecution Authority (NPA) confirmed in a statement that Kayishema "has abandoned his bail application and will instead launch an asylum application today."
"My instructions are to apply for asylum in the Republic of South Africa which will indeed be attended to before close of play today," lawyer Juan Smuts told AFP after accused mass killer Fulgence Kayishema appeared in court in Cape Town.
Smuts said his client "fears for his life, if and when extradited."
The asylum application is likely to delay Kayishema's trial and "will suspend his extradition as envisaged," said the lawyer.
There have not been any formal extradition requests so far.
Kayishema is described by the International Residual Mechanism for Criminal Tribunals (MICT) - the successor to the U.N. court that prosecuted scores of major suspects - as "one of the world's most wanted genocide fugitives."
Kayishema allegedly took part in one of the Rwanda genocide's bloodiest episodes,
in which he and others allegedly murdered more than 2,000 men, women and children who had taken refuge in a Catholic church in Nyange, Kivumu District.
He is one of four remaining fugitives sought by U.N. investigators for their role in the genocide, was arrested last month in the town of Paarl in South Africa's Cape Winelands region.
The 62-year-old, who used many aliases and false documents during 22 years on the run, faces 54 fraud and immigration-related charges in South Africa.
But state advocate Nathan Adriaanse said in court that new evidence has emerged which will result in new charges being added.
He is expected back in the Cape Town court on August 18 for what the NPA said was for "further investigation."
The former Rwandan police inspector was arrested on May 24 in the small town of Paarl, 60 kilometres (35 miles) north of Cape Town.
The hunt for Kayishema spanned countries across Africa, according to the MICT.
The United States had offered up to $5 million reward for information leading to Kayishema's arrest, transfer or conviction, but there have been no details as to whether this played a role in the capture.
The MICT in 2015 took over the work of the International Criminal Tribunal for Rwanda (ICTR), set up by the U.N. after the genocide.
Before handing over the reins, the ICTR sentenced 62 people, including a 30-year term handed to former minister Augustin Ngirabatware, and acquitted 14.
Rwanda started trying genocide suspects in 1996, and on a single day in April 1998 had 22 of them executed by firing squad.
It abolished the death penalty in 2007, lifting the main obstacle for the ICTR to extradite genocide suspects to Rwanda for trial.
Between 2005 and 2012, more than 12,000 community-based courts put nearly two million people on trial and convicted 65 percent, sending most to prison.
Around 800,000 Rwandans, most of them ethnic Tutsis, were slaughtered over 100 days at the hands of Hutu extremists.