That exodus sharply increased the number of Syrians now living in neighboring countries, bringing the total number of refugees to 234,368 in the past 17 months, the agency said.
Along with activists' reports that the death toll in August was also the highest in the civil war with 5,000 killed, all signs are pointing to unprecedented levels of misery in a country where President Bashar Assad's regime is fighting an increasingly violent rebellion.
"If you do the math, it's quite an astonishing number," U.N. refugee agency spokeswoman Melissa Fleming said of the number of people who fled in August, speaking to reporters Tuesday in Geneva.
"And it points to a significant escalation in refugee movement and people seeking asylum, and probably points to a very precarious and violent situation inside the country," she said.
But even the August figure only counts refugees who are registered and those awaiting registration. Officials acknowledge the real number of Syrian refugees is likely way above 200,000, because tens of thousands are believed to have not yet contacted authorities.
The uprising began with largely peaceful protests of Assad's regime but has turned into a civil war that activists say has killed at least 23,000 people.
As Syrians look to escape the bloodshed, Assad told the head of the International Committee of the Red Cross on Tuesday that the group is welcome to operate in Syria - as long as it remains "neutral and independent," state media reported.
Assad has accused the international community of conspiring to unseat him.
ICRC spokeswoman Rabab al-Rafai did not give further details about Assad's meeting with Peter Maurer in Damascus but said the Red Cross chief also met Deputy Foreign Minister Faysal Mekdad and the head of the Syrian Arab Red Crescent.
"President Assad confirmed Syria welcomes the humanitarian operations that the organization is conducting on the ground in Syria as long as it works in a neutral and independent way," the state-run SANA news agency quoted Assad as saying.
Maurer's three-day visit, which began Monday, comes as the need for humanitarian assistance grows increasingly urgent.
According to the U.N. refugee agency, there are now more than 80,000 Syrian refugees in Turkey, where the borders remain open, and there is a backlog of 8,000 Syrians waiting to be processed at the border, Fleming said. Jordan has more than 77,000 Syrian refugees; Lebanon has more than 59,000; and Iraq nearly 18,700, according to the agency.
Inside Syria, the fighting has spread to the two largest cities - the capital of Damascus and the commercial hub of Aleppo.
The U.N.'s World Food Program spokeswoman Elisabeth Byrs said more than 264,000 people are taking shelter in public buildings in the Aleppo region - about 200,000 in rural areas and more than 64,000 in the city.
Byrs said her agency is scaling up operations to provide food urgently needed by 1.5 million people this month, mainly in areas where there has been fighting and people have been made at least temporarily homeless.
Abdul-Qadir Saleh, the commander of the Tawhid Brigade that is spearheading the Aleppo offensive, said rebels control most of the city, Syria's largest.
"The regime only controls 30 percent of Aleppo," Saleh told reporters in Istanbul. He added that regime forces are attacking certain sites to try to "turn civilians against the rebels."
Saleh's claim could not be independently verified, and the government says its troops are advancing in the city.
Activists also reported scattered violence in Idlib in the north, in Daraa in the south and in the Damascus suburbs.
The head of the main Syrian opposition group called for a massive aid program to help rebuild his country in a post-Assad era, warning that a lack of economic development would open the door to extremism.
Abdelbaset Sieda, the head of the Syrian National Council, told a meeting of Syrian opposition representatives and diplomats that a reconstruction program similar to the one after World War II would be needed.
Assad's regime has devastated the public finances and institutions to such an extent that Syria won't be able to rely immediately on oil revenues and taxes to rebuild, Sieda said in Berlin.
The working group on economic rebuilding, which Germany chairs with the United Arab Emirates, is designed to address how to prevent the collapse of basic services and infrastructure and how to revive the economy in a post-Assad Syria.
Unlike neighboring Iraq, Syria lacks vast oil reserves that could kick-start the economy and help finance the reconstruction of infrastructure damaged in the fighting.
Syria used to produce about 380,000 barrels of oil a day, of which 250,000 were for local consumption and 130,000 for exports. By comparison, oil giant Saudi Arabia produces about 10 million barrels a day.
A fifth meeting of the U.N.-sponsored Syrian Humanitarian Forum - made up of hundreds of nations, regional groups, U.N. agencies and non-governmental organizations - is planned for Friday in Geneva. At the last meeting in July, the operations director for the U.N.'s humanitarian office said its appeal for $189 million to help people inside Syria was only 20 percent funded.
Heilprin reported from Geneva. AP writer David Rising contributed to this report from Berlin.