Speaking at a meeting of the United Nations refugee agency, they have pled for more financial assistance and for other countries to take a greater share of the refugees.
And the Australian president of the UN Security Council says it hopes last week's consensus on Syria's chemical weapons can lead to a joint statement on increasing aid to those still in Syria.
The flurry of activity on Syria comes as the United Nations estimates the conflict has left more than 100,000 dead -- so far.
Ildi Amon reports.
More than two million Syrians -- mostly women and children -- have fled Syria since the conflict there began with a crackdown on demonstrations in early 2011.
This week, the United Nations High Commissioner for Refugees has met in Geneva to discuss how it can better support those flooding into neighbouring countries.
UN High Commissioner for Refugees Antonio Guterres told delegates the implication of the unprecedented movement of people will be felt globally.
"This crisis has gone far beyond requiring only humanitarian assistance to displaced people. The Syrian conflict is not just a threat to global peace and security, but it results in fundamental, structural problems for the countries of the region. They are going through huge demographic changes following the refugee influx, unsettling their social and economic fabric."
UNHCR figures show 700,000 registered Syrian refugees in Lebanon alone.
But Lebanon's social affairs minister says the true figure is actually much higher because a large proportion of refugees do not register with the United Nations.
Abu Faour says there are actually 1.3 million Syrian refugees living in Lebanon, about 30 per cent of his country's population.
And he says Lebanon is increasingly frustrated with the lack of support from the international community.
Mr Faour says the burden on the country's fragile infrastructure and its school and health systems is also creating antagonism against the Syrian refugees.
Elsewhere, more than 525,000 Syrian refugees have fled to Jordan, with its Zaatari camp alone sheltering some 100,000 people.
The UNHCR figures, which tally registered refugees only, also indicate Iraq and Egypt have more than 100,000 Syrian refugees each.
And they show Turkey's 21 refugee camps are housing half a million people.
At the special meeting of the U-N refugee agency, Turkey's Foreign Minister, Ahmet Davutoglu, called on the UN to support those countries with financial and development assistance.
"The situation in Syria deteriorates further every day. The humanitarian calamity we face now is beyond our individual capabilities. It requires collective approaches as well as joint actions."
Mr Davutoglu also called on other countries in the Middle East and in Europe to grant asylum to more Syrians who have fled their homeland.
Meanwhile, the Australian president of the UN Security Council says it hopes its members will agree to demand the Syrian government allows immediate access to the country to provide aid.
Millions of people inside Syria are in need of humanitarian help.
The Security Council president and Australian ambassador to the United Nations, Gary Francis Quinlan, says he hopes a joint statement would urge Syria to allow cross-border aid deliveries.
And he says he hopes such a statement would also urge parties to the conflict to hold humanitarian pauses in the fighting.
Mr Quinlan says he hopes the diplomatic unity between Russia and Western powers on the Syrian chemical-arms resolution last week might extend to the aid statement.
But it is not clear whether a consensus will be achieved, with Russia saying it would only agree to the cross-border access if Syria agreed.
And Syrian diplomats say they oppose cross-border access because of concerns weapons could be smuggled to opposition forces.
But Mr Quinlan says the momentum is now there for a unanimous statement.
"There is a sense -- and has been for quite a while -- that we needed to act more quickly on the humanitarian situation. And, frankly, if it hadn't been for the incident in Damascus on 21 August, which obviously then caused us all to focus on the chemical-weapons issue as an immediate issue which needed to be addressed, I think we would have been talking about a humanitarian product -- a statement -- a couple of weeks earlier than we are. But speed is of the essence, and we are committed to trying to get a result as soon as we can in the next few days."
Meanwhile, Syria's Foreign Minister, Walid al-Moualem, has addressed the UN General Assembly, saying Syria will fulfil its obligations in destroying its chemical weapons.
That comes as UN chemical-weapons inspectors have left Syria, ending their second mission there in two months.
Another team of UN experts tasked with starting the process of verifying and destroying Syria's chemical weapons is expected to arrive later this week.
Mr Moualem told the General Assembly the Syrian government is working with the UN to meet the basic needs of Syria's citizens.
But he says foreign sanctions are contributing to the humanitarian need in his country.
And he also used the forum to call on those refugees who have fled Syria to return home.
"It should be noted here that a great number of our people were forced to resort to some neighbouring countries due to the activities of armed groups in border areas. Regrettably, those displaced Syrians were put -- in some countries -- in military training camps or in what resembles places of detention. I appeal on this platform to Syrian citizens to return to their towns and villages, where the state guarantees their safe return and their livelihoods away from the inhuman conditions they suffer in such camps."
Feature by Ildi Amon
