The Syrian cab driver tolerated beatings, arrests and daily indignities during the country's 16 months of turmoil.

But after a rocket struck his house in the Daraa province city of Herak last week, the man and his family finally had enough.

The 29-year-old Sunni man, his wife, two young daughters and other relations left their homes on July 16 and embarked on a journey at night to the nearby Jordanian border.

He was among the more than 120,000 people who've fled to the neighboring countries -- Turkey, Iraq, Lebanon and Jordan -- to escape the warring in Syria.

The U.N. High Commissioner for Refugees, Antonio Guterres, on Friday expressed his growing concern for the dramatic flight.

"With the spread of deadly violence, I am gravely concerned for the thousands of Syrian civilians and refugees who have been forced to flee their homes," Guterres said.

The driver's story punctuates the misery across the restive nation, engulfed in what is now regarded as a civil war between Syrian President Bashar al-Assad's government and its foes.

The cabbie is one of millions who have had to wrestle with whether they should brave staying or resort to leaving. The man, who answered questions from CNN via translators at the Bashabsheh resettlement camp in Jordan, didn't want his name used. But he cited many factors that led to what was a spontaneous trip to the border.

"It had been increasingly difficult to work as a driver due to stricter and more frequent road checkpoints and fear of random arrests and imprisonment," he said. "Everybody in Daraa is being targeted by Syrian security because the revolution started there."

The miseries of daily life hit home, he said. "Shopping for milk for the children was risky. Medical care became inaccessible."

He had been apprehended twice, once in June 2011 when he was arrested in his taxi at a checkpoint and beaten up while taking a man to visit his wife, in labor at a hospital. Two months later, he was arrested while waiting in his taxi for three men in a money-exchange shop. Security officers accused the three of arranging a demonstration. They arrested the men and the taxi driver. The driver was beaten up.

He was scared about the psychological well-being of his daughter, growing anxious over the sounds of gunfire and war. He thinks that his participation in peaceful demonstrations may have put him at great risk. He and his family, along with two of his sisters and their children, went to an assembly where the Free Syrian Army helps fleeing Syrians.

Women and children traveled to the border in vehicles and the men walked as the Jordanian army waited for them to arrive.

The cab driver said he and the other refugees regularly commiserate about life.

"The greatest difficulties are leaving houses, their country and their life. It is difficult to accept, but there is no choice because of the children," the driver said. "Seeking asylum is the worst thing in life."

U.N. refugee officials, neighboring governments and non-governmental agencies have been working to help refugees, and the United Nations recently launched a drive for $193 million to help refugees. The plan has received about a quarter of the amount needed.

Syrians have been trickling out of the country during the conflict but those numbers have tripled since April, the U.N. refugee agency said.

The latest U.N. number is that as of Wednesday, 120,000 have sought protection but the refugee agency says the local governments count many more.

The number of Syrians now in camps in Turkey has surpassed 43,000, disaster and emergency officials from that country said.

The U.N. refugee agency said recently it has registered well over 30,000 in both Lebanon and Jordan. But the flight is fluid. There are reports of 8,500 to 30,000 people crossing into Lebanon in a two-day period. More than 8,000 have crossed the border into Iraq.

"I am extremely grateful Jordan, Lebanon, Iraq and Turkey have maintained open borders," Guterres said.

One irony is that Iraqis who had fled to Syria because of war and instability have been touched by the unrest. Some, for example, have had to flee the Damascus suburb of Seida Zeinab, and an Iraqi family was found dead in Damascus.

"I fear for the civilians caught up in the violence in Damascus, including the large Iraqi refugee population residing there," Guterres said.

Iraqi Prime Minister Nuri al-Maliki deplored the attack against Iraqis and urged his fellow citizens to return. He said on Friday those who don't "have blood on their hands" will be forgiven, a reference to violence during the war.

"We appeal to the United Nations to intervene promptly and in cooperation with the Syrian authorities to protect Iraqis and help them and to facilitate the process of return to Iraq," he said.