"We all know of the terrible, thoughtless, ignorant act that someone perpetrated in this city yesterday," said Mayor Michael Nutter. "We will, of course, at some point in time find the coward."
Pork and pork byproducts are haram, or forbidden, in Islam.
Surveillance video shows a red truck driving by the mosque. On its second pass, someone tosses something from the vehicle and what appears to be the pig`s head rolls near the mosque`s door.
The driver and the passenger of the vehicle are not visible.
"It is too early in the investigation to determine if it is a hate crime, but I anticipate that will be the direction the investigation will go," Philadelphia police officer Leeloni Palmiero told CNN.
Police are investigating whether the incident has any connection to a voicemail the mosque received last month, in which a male voice said: "Are you happy about what happened in France?" "God is a pig!" and "God is Pork!"
The FBI has launched a parallel investigation.
At his Tuesday news conference, Nutter blasted Republican presidential candidate Donald Trump, who recently proposed a ban on Muslims entering the United States.
"What we`re finding is that no group is safe from his ignorance and rhetoric," said the mayor, who later called Trump an "asshole."
Ibrahim Hooper, national communications director for the Council on American-Islamic Relations, told CNN that his group has seen a spike in violence and anti-Muslim sentiment since last month`s terror attacks in Paris.
"The anti-Muslim atmosphere we`ve been seeing in recent weeks is, in many ways, worse than it was after the 9/11 attacks," he said. "After 9/11, the anti-Muslim rhetoric was on the fringes. ... Now it`s at the mainstream."
In his experience, mosque spokesman Marwan Kreidie told CNN that the incident involving the pig`s head is unusual. He described the neighborhood where the Al-Aqsa Islamic Society is located as tolerant and diverse.
When asked about Trump, he said that "words have consequences," but stressed that the problem is not contained to one person.
"Unfortunately, there appears to be an audience for this," said Kreidie.
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