The UK-based Syrian Observatory for Human Rights says 539 people have been killed since protests calling for political reform began on 15 March.
Mr Hague said the Syrian government needed to respond with "reform not repression".
President Bashar al-Assad's government blames extremists for the unrest.
Activists say at least six people were killed by security forces in the southern city of Deraa on Saturday.
They also said more than 60 protesters were killed across the country on Friday - more than half of them in Deraa.
Officials said the number of dead was far lower, and included four soldiers. They say 80 security personnel have been killed in the unrest.
Foreign journalists are not being allowed into the country, and the exact picture of what is happening remains unclear.International community
In a statement released on Saturday, Mr Hague said he was "extremely concerned by ongoing violence and repression."Continue reading the main story
I welcome the EU's decision to accelerate work on targeted measures against those responsible”End Quote William Hague Foreign Secretary "There are credible reports that over 500 people have been killed in recent weeks," he said.
"The Syrian government has failed to heed repeated calls by the international community for restraint. As I have stressed it is vital to respond with reform not repression."
On Friday, the UN Human Rights Council condemned the violence, in a US-led resolution by 26 votes to nine with seven abstentions.
The council, based in Geneva, said it would ask the UN Office of the High Commissioner for Human Rights to dispatch a mission to investigate "all alleged violations of international human rights law and to establish the facts and circumstances of such violations and of the crimes perpetrated".
Nations demanded that President Assad's government stops the violence, releases political prisoners and lifts restrictions on the media and access to the internet.
Mr Hague welcomed the UN resolution and also the European Union's decision to launch an arms embargo against Syria and to review all EU co-operation with the country.
"We will continue to work with our partners to ensure that those responsible for the violence are held personally to account," he added.
"In this context, I welcome the EU's decision last night to accelerate work on targeted measures against those responsible. The United Kingdom will again be in the forefront of pushing for such measures."
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