By the CNN Wire Staff

(CNN) - Members of the Joplin, Missouri, mosque destroyed by a suspicious fire are sad and shaken, but resolute in their plans to stay in the area, a spokeswoman said Tuesday.

"This is a very close-knit community," Kimberly Kester said on CNN's "Early Start." "I think we feel secure and nobody's going to move away because of this action."

A fire that broke out early Monday destroyed the worship house of the Islamic Society of Joplin, a small mosque serving about 50 families in the southwest Missouri city.

The mosque's community is no stranger to attacks, Kester said.

"We've had our mailbox destroyed. Our sign was burned. The sign has been shot with guns. People would sometimes drive by and yell at us," she said.

On July 4, a surveillance camera caught a man throwing some sort of incendiary device onto the building. The resulting fire damaged part of the roof.

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Monday's fire burned the mosque to the ground. Carl Junction Fire Chief Bill Dunn said the structure was a complete loss.

Federal agents are investigating Monday's fire, FBI spokeswoman Bridget Patton told CNN.

"If it is determined that the fire was deliberately set or intentionally set, then we will investigate it to the full extent possible," Patton said.

The FBI, in conjunction with the Bureau of Alcohol, Tobacco, Firearms and Explosives, has issued a $15,000 reward for information in the July incident.

iReport: Joplin Mosque Tragedy

In Monday's fire, which has not yet been officially labeled arson, the Council on American-Islamic Relations has offered a $10,000 reward for information.

Kester declined to say if mosque members believe the same person is behind all of the attacks. She said they're confident investigators will get to the bottom of what happened, even though the mosque's security cameras were destroyed in the fire. She said police have always taken previous complaints very seriously.

"Right now we don't want to jump to any conclusions and we don't want to lay blame on anyone," Kester said. "We're putting our trust in the police force and the firefighters, the investigators, that they will find this person."

The fire, which happened during the Muslim holy month of Ramadan, has been unsettling for mosque members, Fauzia Iqbal told CNN affiliate KYTV.

It's frightening, Iqbal said, and "there is a lot of shock and disbelief... because we don't expect this kind of behavior from our fellow citizens."

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Kester said that members of the mosque have received "an outpouring of support" from the Joplin community.

Among other things, St. Philips Episcopal Church in Joplin has offered to open its doors to the mosque's members so they have someplace to pray, KYTV reported.