The department has so far placed some 1,300 in the US, acknowledging that it is way behind the projected schedule that was first set by Obama in September, the Hill reported Saturday.
Lack of personnel to interview the refugees is one of the problems the department said is slowing down the process.
The State Department is now performing a "surge operation" to process the rest of the Syrian refugees in Amman, Jordan, over a three-month period, giving them enough time to get to the US before September.
Larry Bartlett, the State Department's director of the Office of Refugee Admissions, said recently that the department has devoted more staff in Amman to speed up the process while hiring new employees for the job.
According to one spokesperson, the State Department has interviewed about 9,500 refugees in Amman since February 1, and 12,000 more interviews should be completed by April 28.
The total number of Syrians in Jordan is more than 1.2 million, including those who arrived before the conflict began in 2011.
A large number of Syria's 22-million population has fled the years-long conflict in the country.
Washington's refugee intake is much smaller than some European countries such as Germany whose total refugee admissions have raised to hundreds of thousands.
The current small numbers, however, have already provoked a significant backlash in the US, mostly from Republican politicians who believe the admission puts the US national security at risk.
"It's clear that ISIS (Daesh) wants to, has planned on attempting to infiltrate refugee populations. This is a problem. If one person gets through who is planning an attack in our country, that's a problem," House Speaker Paul Ryan said Thursday.
This is while supporters of the program say the US is doing the right thing as more than 4.7 million Syrians have registered with the United Nations High Commission for Refugees (UNHCR).
The plan to bring in more refugees has been met with stiff opposition in the ongoing presidential race, with Republican presidential front-runner Donald Trump calling for a temporary ban on Muslim immigrants and fellow candidate Texas Senator Ted Cruz proposing a religious test on refugees.
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