The figure, due to be officially released in the coming days, is a dramatic rise on earlier estimates by the UN High Commissioner for Refugees of some 2.5 million displaced living in precarious conditions inside the country.
It also adds to the 1.2 million refugees who have streamed across borders into neighboring countries, placing a huge strain on governments in Jordan, Turkey and Lebanon who have kept frontiers open.
With almost a quarter of Syria's population of around 22.5 million now in flight, the two-year conflict is wreaking a huge toll on civilians caught in cross-fire as opposition forces seek to topple President Bashar al-Assad.
"What we're seeing... is that now it is not just violence that is driving flight," US Deputy Assistant Secretary for Population, Refugees and Migration Kelly Clements told AFP.
"It is also just a decline in livelihoods, a decline in the economic means for families to be able to support themselves. It's disruption to services, it's kids not being able to go to school, it's water systems that have been either cut off or somehow affected."
Health services, bakeries, schools, vital components of normal life are teetering or have shut down, leaving a population in distress.
Those who could flee have already gone, leaving the most vulnerable to fend for themselves, many of whom have now been forced to relocate two or three times as the fighting has shifted and swelled.
Aid agencies themselves have lost team members killed in the fighting, while UN-led operations to try to get assistance across battle lines have proved dangerous and complex involving delicate negotiations.
"Really the most pressing challenge for all of us is just how dangerous and unpredictable the security environment is and the need for greater access," said Nancy Lindborg, assistant administrator for the US Agency for International Development (USAID).
Working through partners such as the World Food Program, the United States has sponsored programs such as providing flour to bakeries in northern Aleppo -- enough to feed some 210,000 people for the next five months.
With the UNHCR they are trying to provide shelter, tents and blankets, to communities of displaced people hunkered down in schools or public buildings and cut off by the fighting.
The US has also focused on health and medical needs. Although initially the aim was to train doctors to deal with battle injuries, increasingly they are filling the gap providing basic health care as hospitals crumble.
They are also working with the local Syrian coordination councils in liberated areas to help rehabilitate schools to get children, some of whom have lost two years of education, back into the classroom.
Initial figures of 2.5 million displaced in the country drawn up earlier this year "no longer reflect the quickly evolving situation," UNHCR regional public information officer Reem Alsalem acknowledged.
The UN is revising its planning and scenarios and believes now that the number of internally displaced people inside the Syria "is around 4 million," she said in an email.
"There is this sense of lives interrupted, in addition to the deprivation and trauma," said Lindborg. "You were a law student yesterday and today you're a refugee. And it's that human dimension that sometimes gets lost."
The United States has so far provided some $385 million for humanitarian aid, of which nearly $216 million has been spent on needs inside Syria, with some 60 percent going to opposition-held areas.
Top UN officials have warned that with no end in sight to the fighting, each of Syria's neighbors could be hosting a million refugees by the end of the year -- an enormous burden on already-stretched economies.
Donors at a Kuwait conference in January pledged some $1.5 billion in aid -- of which $520 million was specifically to help people trapped inside Syria, with the rest going to help the nations hosting refugees.
But to date only about 30 percent of the funds have actually been received.
"The planning figures of this appeal, which went until the end of June, is only 30 percent subscribed, and yet we've already surpassed the needs that were articulated in that appeal," said Clements.
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