The figure for operations inside Syria was $1.4 billion.
"If the fighting doesn't stop, we risk an explosion in the Middle East for which the international community is not prepared," UN refugee agency head Antonio Guterres told reporters.
"It is not only a matter of generosity but also of enlightened self-interest."
More than 94,000 people have been killed and some 1.6 million Syrians fled the country since the civil war began in March 2011 after President Bashar al-Assad cracked down on protests against his regime.
The number of refugees is expected to reach at least 3.45 million by the end of this year, according to the UN appeal.
Within the country, 6.8 million people are forecast to need aid this year, the majority of them having been forced to flee their homes because of the fighting.
Government forces were trying on Friday to mop up final pockets of rebel resistance north of Qusayr, the central town near the border with Lebanon that they retook on Wednesday bolstered by fighters from Lebanon's Shiite movement Hezbollah.
At the United Nations, Russia agreed to a Security Council statement demanding that its ally Syria allow humanitarian access to Qusayr.
The Syrian Observatory for Human Rights said the army was bombarding another rebel bastion to the north of Qusayr to which hundreds of wounded and civilians had fled.
"Four rebels were killed on Thursday night trying to evacuate the wounded" in eastern Bweida, Observatory head Rami Abdel Rahman told AFP.
He said the army was "leaving no way out for rebels, civilians or the wounded" in its campaign to control the whole Qusayr region.
The Observatory also reported that Assad's forces were sending reinforcements to Aleppo province in northern Syria, where large swathes of territory have been in rebel hands for months.
The army's preparations for a new offensive in the north came a day after a brief rebel seizure of the Quneitra crossing on the armistice line separating Israeli and Syrian troops on the Golan.
That violence prompted Austria to announce it was withdrawing its 377 troops from the 1,000-strong UN Disengagement Observer Force.
UNDOF peacekeepers from the Philippines and India were wounded by mortar shrapnel in fighting for the strategic crossing, according to UN diplomats.
Manila said it too was considering pulling out its 341-strong contingent.
UN leaders held emergency talks late on Thursday to replace the Austrian troops who make up more than a third of UNDOF, which has monitored a ceasefire between Israel and Syria since 1974.
President Vladimir Putin proposed that Russian peacekeepers replace the departing Austrian troops ahead of a meeting of the UN Security Council on the UNDOF crisis on Friday.
However, UN spokesman Martin Nesirsky said this was not possible because Russia is one of the five permanent members of the UN Security Council.
"We appreciate the consideration that Russia has given to provide troops on the Golan. However, the disengagement agreement and its protocol between Syria and Israel does not allow for the participation of permanent members of the security council in UNDOF," Nesirky told reporters.
Any deployment of Russian troops would be deeply unpopular with the Syrian rebels who have been angered by Moscow's steadfast support for its ally Damascus.
In neighbouring Lebanon, the army warned that a plot was being hatched to embroil Lebanon in the Syrian conflict, as fresh clashes linked to Syria in the northern port of Tripoli killed one person.
And two journalists working for a French radio channel have gone missing in Syria, with no word from them in 24 hours, their employer Europe 1 said.
French President Francois Hollande called on Friday for Didier Francois, a seasoned reporter in trouble spots, and photographer Edouard Elias "to be freed immediately."
And an Austrian man with dual Syrian citizenship arrested by Syrian intelligence in December while distributing aid has been freed and is on his way back to Austria, his family said.