United States intelligence fears that as many as 30,000 foreign fighters have travelled to Iraq and Syria since 2011, many of them to join the Islamic State (IS) group.
The number reportedly includes many westerners, among them perhaps 250 Americans, and represents a doubling of last year's US assessment.
The New York Times report cites anonymous "intelligence and law enforcement officials" in its report.
Moreover, a congressional report due out this week was expected to suggest that a year of US-led air strikes has not slowed recruitment.
Meanwhile, US president Barack Obama will chair an international summit this weekend on the sidelines of the United Nations General Assembly for leaders fighting the IS group and "violent extremism."
US and Western diplomats are scrambling to cobble together a diplomatic strategy to end the war in Syria after the latest humiliating blow to their military plan.
To that end, US Secretary of State John Kerry and his European counterparts reached out to the West's traditional foe, Iran, at the General Assembly in New York this weekend.
Iran and Russia back the Syrian president, Bashar al-Assad, whom Washington sees as the instigator of a civil war that has left half his country in the hands of the Islamic State group.
Unwilling to countenance a peace process that would leave Mr Assad in power, the US has backed small "moderate" rebel groups.
US strategy shredded
But that strategy appeared to be in tatters on Saturday after the Pentagon admitted the latest US-trained fighters to cross into Syria had given a quarter of their gear to al-Qaeda.
A previous 54-strong group that crossed into northern Syria earlier this year was attacked by al-Qaeda's local franchise, the Al-Nusra Front, and fell apart, leaving only four or five guerrillas active.
In contrast to the poor US effort to shore up its allies on the ground, Russia and Iran have proven good friends to Mr Assad.
Iran has dispatched Shi'ite militia fighters and Russia has deployed a powerful military presence to a base on Mr Assad's territory.
Mr Kerry and his allies are hoping to persuade Tehran and Moscow to push for a broad political solution to the conflict.
"I view this week as a major opportunity for any number of countries to play an important role in trying to resolve some of the very difficult issues of the Middle East," Mr Kerry said at a joint appearance with the Iranian Foreign Minister Javad Zarif.
According to an EU statement, Mr Zarif said Iran would assist United Nations-led efforts to broker a political compromise that would end the civil war in Syria.
Mr Kerry is also due to meet Russian Foreign Minister Sergei Lavrov on Sunday, and Mr Obama will see the Russian President, Vladimir Putin, during a packed General Assembly programme.
Meanwhile, a ceasefire in northwest Syria, that is part of a wider deal including cessation of hostilities in the area as well as in a town near the Lebanese border, has been broken.
Shells apparently fired by insurgents hit the village of al-Foua in the northwestern province of Idlib, according to the Syrian Observatory for Human Rights.
Rebels had earlier blamed government forces for violating the ceasefire by dropping barrel bombs nearby.
Warring sides had agreed on a ceasefire in al-Foua and next-door Kefraya, two villages held by pro-government forces and besieged by rebels, as well as in the town of Zabadani near the Lebanese border, where insurgents are holed up and surrounded by government forces.
- Reuters, AFP