Oxfam says that some 670,000 people have left Syria since the crisis began in March 2011 but numbers have risen recently. In Jordan alone, the number of people crossing daily trebled in the past week.
The cold weather has seen an increase in the number of those suffering respiratory infections and pneumonia, according to the aid agency, which is distributing mattresses, blankets, heaters and gas oil to help new arrivals.
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The president's former lawyer had pleaded guilty to charges including breaking campaign finance laws, lying to Congress, and tax fraud.