The "security concern" for the UK posed by individuals who have trained and fought in Syria is "a big problem" for MI5 and the police, the country’s immigration minister told the BBC on Sunday.
James Brokenshire said "a significant and growing proportion" of resources was spent on the issue.
He said it was right to be "vigilant" about travel between the UK and Syria.
The comments come in the wake of a report in The Sunday Times which said that security services are "closely monitoring" 250 British-based jihadist linked to Syria.
The authorities are concerned that such people may be radicalized and militarized - and urged by those whom they come into contact with in Syria to turn their attentions away from the Syrian regime and instead attack targets in the West.
The civil war in Syria has attracted rebel groups with links to Al-Qaeda, such as the Al-Nusra Front and the Islamic State of Iraq and the Levant (ISIS). In addition to fighting President Bashar Al-Assad’s forces, these groups have been fighting the more moderate rebel groups in what has turned into a second war.
These Al-Qaeda-linked groups have been heading to war-torn Syria from many other countries since fighting broke out in 2011.
Last week, a video was posted online showing British man Abdul Waheed Majid, who is thought to have carried out a suicide bombing in the city of Aleppo.
Speaking to the BBC, Brokenshire said he believed the "security concern" linked to Syria was "likely to be with us for the foreseeable future."
"A significant proportion and a growing proportion of the security services work is linked to Syria in some way," he told the network.
"This is a big problem that the security services and the police are actively focused on,” added Brokenshire. "It's why they are vigilant, why they are taking the steps that they are around the border and monitoring travel to and from Syria in the way that they are."
The immigration and security minister said Syria had become "the number one jihadist destination in the world" and the number of Britons thought to have travelled there to fight so far was in the "low hundreds."
Brokenshire said he recognized "that not everyone who has been to Syria and is travelling back is involved in terrorism", but added, "Clearly the message is: 'People shouldn't be travelling.'”
The Sunday Times report said that the number of individuals being monitored by MI5 and the police is much higher than previously reported, underlining "the growing danger posed by 'extremist tourists'".
In December it was reported that Britain has been revoking the citizenship of its nationals who join the Syrian civil war, in an attempt to prevent its nationals from returning home and bringing fundamentalist Islam with them.