CNN would allow vice president to take part even if he declares his campaign the day of the event.
A quarter of Americans who are registered Democrats or lean that way said Biden now is their top choice for president.
The pontiff this week will visit New York City, Philadelphia and Washington.
"We're just not quite there yet, and I may not get there in time to make it feasible to be able to run," he said.
Meanwhile, Israel debates its response to refugee crisis.
Alex Salinas, a 21-year-old Spanish transgender man, was denied his request to become his nephew's godfather by the Vatican's Congregation for the Doctrine of the Faith.
William Joseph Levada was arrested for DUI on Hawaii's Big Island and released on $500 bail.
The Pope listed 15 "diseases" afflicting the highest-ranking members of the Catholic church.
American bishops vote in Baltimore this week on who will represent them at next year's synod in Rome. Their choices will speak volumes.
A new report released by the Vatican Monday suggests a softening in tone—if not in policy—toward gays and gay marriage.
Northern Ireland's firebrand preacher turned peacemaker dies