The Council on American-Islamic Relations on Friday asked for an apology from KFI-AM 640 host Bill Handel, who allegedly made fun of the deaths during a 12 January segment he called the "Annual Stampede Report".
A spokeswoman for KFI, which is owned by Clear Channel Communications, did not immediately return a message left on Thursday.
Handel's producer, Michelle Kube, also did not return calls for comment. Handel had left work for the day and attempts to reach him were unsuccessful.
At least 363 pilgrims were killed and hundreds injured in a stampede on 12 January near Makka, where thousands of people were rushing to carry out a symbolic ritual of stoning three pillars representing the devil in Mina.
According to CAIR, Handel imitated the people screaming and then joked that the Muslims at the pilgrimage should use a helicopter to monitor pilgrimage traffic, as is done in Los Angeles with the freeways.
CAIR quoted Handel as saying, "This is Mahmoud Nolan. Hajj in the Sky. There is an accident ... Ali lost his sandal on the on-ramp to the Martin Luther King Jr. freeway ..."
"This is Mahmoud Nolan. Hajj in the Sky. There is an accident ... Ali lost his sandal on the on-ramp to the Martin Luther King Jr. freeway ..."
CAIR quoting Handel
In March 2004, KFI issued an on-air apology after CAIR filed a complaint with the Federal Communications Commission after a skit that claimed Muslims have sex with animals, do not bathe and hate Jews.
"The deaths of hundreds of people engaged in religious observances is no laughing matter," CAIR spokeswoman Sabiha Khan said in a statement.
"KFI needs to distance itself from Mr. Handel's unbelievable insensitivity by issuing a formal apology and a reprimand."
Islam requires that every able-bodied Muslim should perform the pilgrimage to the holy sites in Saudi Arabia at least once.