Several reports say the neighbourhoods of Bab Amro came under attack in the early hours of the morning, whilst 50 tanks reportedly rolled into the residential area of Sittin.
Assad initially responded to protests against his rule with promises of reform, but he also deployed the army to crush dissent in Deraa in the south, where demonstrations erupted on 18 March, and then in other cities.
The Syrian government insists it is pursuing “armed terrorist gangs”.
EU diplomacy chief Catherine Ashton said Wednesday that the EU is to look at fresh sanctions this week against Assad's regime, having already clamped down on his inner circle.
Asked by members of the European Parliament to explain why Assad's name was not on a list of 13 Syrian officials hit by European Union sanctions, Ashton said "we started with 13 people who were directly involved" in cracking down on protests.
Ashton warned that the Syrian leader that he could be next.
Meanwhile, diplomats at the United Nations say international pressure following the crackdown on demonstrators has caused Syria to abandon its plans to run for a seat on the UN Human Rights Council.
Syria was chosen in January as one of four candidates, alongside India, Indonesia, and the Philippines for seats to be filled by Asia under a convention that stipulates UN bodies be filled by regional blocs.
UN Secretary General Ban Ki-moon on Wednesday urged Assad to heed calls for reform and freedom and to "desist from excessive force and mass arrest of peaceful demonstrators".