Lebanon's population has increased up to 10% because of Syrian refugees, the U.N. agency said.
Jordan's energy, water, health and education services have been severely strained.
Turkey has spent more than $600 million setting up 17 refugee camps, with more under construction.
And Iraq, already grappling with 1 million internally displaced citizens, has taken in more than 100,000 Syrian refugees in the past year.
"We are doing everything we can to help, but the international humanitarian response capacity is dangerously stretched," said Guterres, the U.N. high commissioner for refugees. "This tragedy has to be stopped."
Dozens of countries and groups around the world pledged more than $1.5 billion in humanitarian assistance for Syrians in January. But only $200 million had been received by the end of February, the United Nations said.
The war: Shifting but endless
While the end of the war seems nowhere in sight, the opposition has made notable strides against government forces.
This week, opposition fighters said they captured the major northern city of Raqqa -- the first time rebels have seized a provincial capital.
State-run media responded by saying government forces were battling suspected members of the radical Islamist group al-Nusra Front in Raqqa.
But footage from the city painted a different picture. Children climbed atop a fallen statue of former President Hafez al-Assad -- the current president's father -- and beat the cracked figure with a bat and shoes.
Some attribute the rebels' recent gains to shipments of arms from other countries.
But rebels are still fighting to wrest the largest city, Aleppo, from government hands. They recently took over a military base near the city, but full control of Syria's economic hub remains elusive.
While Damascus remains a regime stronghold, rebel and regime forces are battling very close to the city -- threatening to take the fight to the seat of President Bashar al-Assad's power.
Rebels detain U.N. peacekeepers
Tension brewed Wednesday between the United Nations and rebels after about 30 rebels detained 20 U.N. peacekeepers and refused to let them go.
The rebels say the peacekeepers entered a Syrian village near the Israeli-occupied Golan Heights, an area where peacekeepers should not be and where intense fighting has been raging for days between rebels and government forces.
The rebels say they suspect the peacekeepers were trying to aid their enemy, which is defending the al-Assad regime.
The United Nations confirmed the peacekeepers' detention and said they were on a "regular supply mission." The United Nations offered no further details of that mission but said it is "dispatching a team to assess the situation and attempt a resolution."
Intervention: Global attempts and failures
So far, international attempts to stymie the bloodshed have failed.
Trouble brewed from the beginning, when the U.N. Security Council couldn't unify on an action plan for Syria.
Western countries wanted tougher sanctions against the Syrian government, but Russia and China said they didn't want to meddle in another country's internal affairs.
The United Nations and the Arab League sent two seasoned diplomats -- Kofi Annan and Lakhdar Brahimi -- to try to broker cease-fires in Syria, but negotiations never ended the violence.
But the western Syrian town of Tal Kalakh may be a microcosm of hope. There, Syrian forces and rebels have agreed to a cease-fire, brokered in part by a parliamentarian and a sheikh.