The number of refugees fleeing Syria for neighboring nations has risen "well above" 200,000 as the violence intensifies, the United Nations refugee agency said.

"There has been a dramatic increase in the number of [Syrian] refugees in the region during August, we're now at over 200,000 refugees in the region that's over and above our planning figure for all 2012 of 185,000 refugees in the region," said Adrian Edwards, a spokesperson for the UNHCR.

Meanwhile, government forces have been continuing their assault on rebel-held areas across the country.

More than 70 people have been killed in a suburb of the capital, Damascus, in the past three days, activists say. Fighting was also reported in the northern city of Aleppo and the central province of Hama.

Speaking at a news conference in Geneva, Edwards said a record 2,200 people crossed the border to Jordon on Thursday night.

"Further arrivals are expected," he added.

There are currently some 150,000 Syrian refugees in Jordan, according to government estimates.

Turkish authorities said on Friday more than 3,500 Syrians had arrived in the country in the past 24 hours, pushing the total number of Syrian refugees there to more than 78,000.

Some 51,000 Syrians have registered or applied to register with UNHCR in Lebanon, the agency said in a press release. But many thousands more have not yet approached it, UN agency said.