Both London and Paris had warned they were ready to break ranks with their European partners to supply weapons to the rebels as their frustration mounts that diplomacy has failed to end the conflict.
But there appeared little appetite among other Europeans for lifting the ban, many fearing that a flood of weapons into Syria will only escalate the bloodshed.
Austrian Chancellor Werner Faymann said Vienna was not prepared to lift the ban. "We think the delivery of arms does not contribute to a possible solution," he told reporters.
A Spanish diplomatic source said there was widespread hesitation about arming the rebels.
Under the rallying cry "Two years of sacrifice towards victory," protesters on Friday held anti-regime protests in several areas of the strife-torn country including Damascus, Aleppo in the north and Daraa in the south.
"Long Live Syria! Down with (President) Bashar al-Assad!" chanted demonstrators in the village of Harra in Daraa, the cradle of the revolt, activists said, adding that regime forces shelled the village.
"Despite all the killing and destruction, I have hope for the country," said Abu Ghazi, an activist in the flashpoint central city of Hama. "Two years into the revolution, we realise how far we have come."
The main opposition National Coalition pledged on the anniversary to "continue the struggle of those who sacrificed their lives for our vision," and rebel chief Selim Idriss vowed that insurgents will fight on until the regime falls.
"We will not stop fighting until our dream of a democratic country comes true, by bringing about the fall of this criminal regime," said the head of the mainstream Free Syrian Army.
The conflict erupted on March 15, 2011 when protesters inspired by Arab world uprisings took to the streets of cities and towns across Syria for unprecedented demonstrations to demand democratic change.
Despite the demonstrators being unarmed, peaceful and including many women and children, Assad's forces unleashed a brutal crackdown, opening fire on them and prompting an ever-growing number to take up arms.
Two years on, Syria is mired in a civil war that has killed at least 70,000 people and forced one million to flee abroad, with millions more missing or displaced, sparking an economic and humanitarian disaster.
-- Risk of regional 'explosion' --
The International Committee of the Red Cross said it was "deplorable" people were getting used to the fact that so many civilians were being killed each day, with a daily tally of between 100 and 200 dead.
UN High Commissioner for Refugees Antonio Guterres said there was a real risk of a regional "explosion" if the conflict was allowed to drag on.
Rebels have seized large swathes of territory, but growing tensions between liberals and moderate Muslims on the one hand, and Islamists on the other, have raised fears of a collapse into a sectarian bloodbath.
The National Coalition plans to meet in Istanbul next Tuesday and Wednesday to elect a prime minister for rebel-held areas of the country, a member said.
The Damascus government suspects neighbouring Jordan of opening its borders this month to weapons purchased by Saudi Arabia in Croatia for the rebels, a Syrian security source told AFP.
"We deplore the change of attitude of Jordan, which in the past 10 days has opened its borders and is allowing to cross over jihadists and Croatian weapons bought by Saudi Arabia," the source said.
The army on Friday resumed an assault on parts of third city Homs infiltrated by the insurgents, including Baba Amr, the Old City and Khaldiyeh, the Syrian Observatory for Human Rights said.
Troops also pounded south Damascus and nearby towns, the Britain-based watchdog said, adding that at least 151 people were killed across the country on Friday, including more than 20 civilians in the capital's province.