CORONA: With tears in her eyes, Mohammad Halisi's young daughter asked her father "Why are we bad?" after seeing reports that a Muslim couple killed 14 people in California last week, and wanted to know whether she should hide the fact she is Muslim from others at her school.

Recalling the conversation while choking back his own tears, the 61-year-old father said he felt frustrated that he and his family were being held responsible for the actions of people he branded "a couple of idiot terrorists".

"It's getting to a point where you have to hide who you are," Halisi said on Friday night at the Islamic Society of Corona-Norco mosque where leaders and law enforcement met to address negative perceptions of the Muslim community. "Seven-year-old kids cannot say they're Muslims because of the bad atmosphere we have."

The mosque is just 40 km from San Bernardino, where United States (US)-born Syed Rizwan Farook, 28, and his Pakistani-born wife Tashfeen Malik, 29, opened fire on his co-workers last week in what the US Federal Bureau of Investigation (FBI) is treating as an act of terror.

Malik had pledged allegiance to the militant Islamic State group on Facebook around the time of the attack and the FBI believes the two had been radicalised for some time.

Muslim Americans across the country have said they are worried about a backlash, as happened in the aftermath of the Sept 11, 2001 attacks.

A handful of incidents at mosques and a rash of anti-Muslim political rhetoric over the last week appear to be compounding their fears of growing Islamophobia.

On Friday, a fire burned the entrance to a mosque in Southern California's Coachella Valley, some 120km from San Bernardino.

A 23-year-old man was arrested on suspicion of arson and for committing a hate crime, the Los Angeles Times reported.

A pig's head was thrown at a mosque in Philadelphia on Monday and a mosque in Jersey City, New Jersey received a letter calling Muslims "evil" and telling them to "go back to the desert".

Several US mosques this year have been subjected to protests by armed groups.

On Saturday, a group of fewer than 10 people, some wearing camouflage and rifles slung over their shoulders, stood outside a mosque in the Dallas suburb of Richardson and held signs and American flags, according to images and reports from local media.

'We feel it more'

US President Barack Obama asked Americans on Sunday to not turn against Muslims after the Paris and California attacks, but rather work with the Muslim-American community in fighting homegrown extremism.

But then Republican presidential candidate Donald Trump ratcheted up the rhetoric on Monday by calling for a ban on Muslim immigrants, students and other travellers entering the country, provoking sharp rebukes across the US political spectrum and from abroad.

Close to San Bernardino, at the Islamic Center of Riverside, where Farook once prayed regularly, members said mosque attendance continued to be low because people did not feel safe.

"Because this happened next door and because our mosque was mentioned, we feel it more," said a 50-year-old Palestinian immigrant who knew Farook but declined to be identified by name.

It is not just Muslims that fear the attacks on Muslims.

Around the corner from the Islamic Society of the Coachella Valley, where Friday's fire occurred, neighbour Israel Orantes said he was concerned about safety, given that it was the second time in about a year the mosque was targeted.

"We are exposed over here," said Orantes, who has lived on what he described as a peaceful, neighbourly street for 14 years. It did not help, he added, that Trump was stirring up animosity with his comments.

"We know we have crazy Muslims, crazy Christians around. They think attacking the mosque is the solution, but we're over here, exposed," he said in front of his home.