Since war broke out between Israel and Hamas last week, a Palestinian-American apparel store owner in San Diego, California, has received a spate of death threats online, she said.

The founder of a chain of Palestinian restaurants in the Northeast U.S., meanwhile, said a person last week screamed expletives at him and his employees at a location in Manhattan, accusing them of being terrorists.

The co-director of an Ontario, California-based clothing company — which sells traditional garments to Palestinians for special occasions — said business has ground to halt because customers are postponing celebrations.

Palestinian business owners in the U.S. and Canada who spoke to ABC News described a swirl of emotions in recent days: Grief for thousands in the region who have died and dread as the death toll continues to grow, fear for themselves or their peers amid an outpouring of hate and the challenge of weathering all of it as they oversee their companies.

However, the conflict has also elicited support from customers or members of local communities, nearly all of the five business owners said, describing notes scribbled on receipts or appended to delivery orders.

“It’s been very heart wrenching and difficult,” Aminah Mufa, the co-founder of the San Diego-based apparel store PaliRoots, who has faced death threats, told ABC News. “I think every Palestinian is unable to sleep right now — we’re sick to our stomachs.”

At the same time, Mufa said, she has drawn encouragement from a simultaneous upswell of compassion for Palestinians. “It has honestly been so hopeful for us,” she said.

The militant group Hamas launched an unprecedented attack last Saturday that has left at least 1,400 people dead and 3,400 people injured in Israel.

In Gaza, 3,000 people have been killed and another 12,500 were injured, according to the Palestinian Ministry of Health.

The U.N. Relief and Work Agency (UNRWA) said that Gaza is running out of body bags, as well as clean water. The Palestinian territory also has no electricity, UNRWA officials said.

Sara Jayyusi, a Palestinian-Candian who runs an online clothing store based in Ontario, Canada, said she mourns the lives lost and worries about the bloodshed likely to come.

A business partner is among those in Gaza, Jayyusi said. “Every day I don’t know if she’s alive,” Jayyusi added.

Jayyusi and her husband run Deerah, a clothing company that specializes in traditional garments worn at Palestinian celebrations. She has received a barrage of threatening messages online, Jayyusi said. “Instagram is a cruel place,” she added.

Meanwhile, sales have plummeted because customers are delaying special occasions amid the war, Jayyusi said. “They’re not in a mental state to really be celebrating,” she said, noting that her husband has begun to look for another job to make up for lost income.

Still, she added, the hardship falls well short of the danger faced by Palestinians in Gaza. “As we all sleep in our homes, Palestinian people are being bombed and starved,” she said.

Israeli officials have said the military is targeting Hamas and attempting to limit civilian casualties. “We are currently striking Hamas in its entirety,” Israel Defense Forces Lt. Col. Peter Lerner told ABC News “This Week” co-anchor Martha Raddatz on Sunday.

Abdul Eleanani, the co-owner of Ayat NYC, a chain of five Palestinian restaurants in New York and Pennsylvania, said the company has faced hateful remarks made to company staff face-to-face and over the phone, as well as an onslaught of negative Google reviews.

Last week, someone walked into the company’s lower Manhattan location at around 10:30 p.m. and yelled, “You guys are terrorists,” while adding an expletive.

The sense of fear has grown after the fatal stabbing on Saturday of a 6-year-old Palestinian boy in Illinois, Eleanani said. “Why did it have to lead to that?” he added.

Alongside the hateful messages, however, the restaurant chain has received far more gestures of solidarity, Eleanani said.

On Instagram, the company posted a photo of a delivery order on which a customer had included a note of support. “My heart is with you all,” the note said. “All solidarity and care to the people of Palestine.” Others have put in orders but asked the restaurant to donate the food to Palestinians instead of delivering it, Eleanani said.

Eleanani said he expects the hateful comments to continue but he remains hopeful.

“The good will overpower the small part of negativity,” he said.

“The purpose of this restaurant and what I’m building around it is just to build awareness of what’s going on back home,” he added. “Palestinians want to live in peace and coexist together.”

ABC News’ Kiara Alfonseca contributed to this report.