More than two million Syrians are now refugees, with the total going up by half a million in the past three months, the UN refugee agency has said.

More than 700,000 have fled to Lebanon, and more Syrians are now displaced than any other nationality, the UNHCR says.

France and the US are continuing to push for military action over alleged chemical weapons use by Syrian forces.

Senior US politicians are set to speak before a congressional committee later to rally support for intervention.

The UNHCR said in a statement on Tuesday: "Syria is haemorrhaging women, children and men who cross borders often with little more than the clothes on their backs."

Around half of those forced to leave are children, UN agencies estimate, with about three-quarters of them under 11.

Just 118,000 refugee children have been able to continue in some sort of education, and only one-fifth have received some sort counselling, with agencies warning of a "lost generation" of child refugees ill-equipped to help rebuild Syria in the future.

Lebanon has received the highest number of refugees, even though it is the smallest of Syria's neighbours and one of the least able to cope.

There is now thought to be one Syrian refugee in Lebanon to roughly every six Lebanese. Jordan and Turkey have taken in the second and third highest numbers respectively.

Pointing out that more than 97% of Syria's refugees are being hosted by countries in the surrounding region, the UNHCR said the influx was "placing an overwhelming burden on their infrastructures, economies and societies".

It once again appealed for "massive international support" to help neighbouring countries deal with the crisis.

International aid agencies are also struggling to cope with the crisis, having only 47% of funds required to meet "basic refugee needs", the UNHCR says.

One of biggest single waves of refugees in the conflict occurred in mid-August, when thousands of refugees from north-eastern Syria poured over the border into Iraqi Kurdistan.

Iraq has the fourth largest population of Syrian refugees, with over 170,000 in the country.

As well as those who have left the country, a further 4.25 million have been displaced within Syria, the UNHCR says, meaning that more Syrians are now forcibly displaced than is the case with any other country.

The UN says the conflict in Syria has caused the world's worst refugee crisis for 20 years, with numbers not seen since the 1994 genocide in Rwanda.

More than 100,000 people are thought to have died since the uprising against Syrian President Bashar al-Assad began in March 2011.

Meanwhile, the French and American governments have continued to set out their case for a military strike in reaction to a suspected chemical weapons attack by Syrian government forces on the outskirts of Damascus on 21 August.

A report presented to the French parliament by Prime Minister Jean-Marc Ayrault on Monday said the assault "could not have been ordered and carried out by anyone but the Syrian government".

The report said the assault involved the "massive use of chemical agents" and concluded that at least 281 deaths could be attributed to it.

In an interview with French newspaper Le Figaro, Syrian President Bashar al-Assad denied being behind the attack, saying it would have been "illogical".

He warned that foreign military action could ignite a wider regional conflict.

The alleged chemical attack took place in the Ghouta, an agricultural belt around the capital on 21 August. The US has put the death toll at 1,429, including 426 children.

The US administration has already presented its case that the Assad regime was behind the attack. The US Congress is due to reconvene next week and will hold a vote on military action at some point after 9 September.

Nato Secretary General Anders Fogh Rasmussen also said on Monday that he is personally convinced that a chemical attack took place and that the Assad government was responsible.

While saying he did not expect Nato to be involved in any action, he said there must be "a firm international response" to deter any future use of such weapons or else it would send a "dangerous signal to dictators all over the world".

Syria is known to have extensive supplies of chemical weapons.

Mr Obama has often said that using them would cross a "red line", prompting US intervention