The Arab League insisted however it would not back down from the operation, which Damascus accepted after weeks of stalling, and said that a new batch of monitors would head to Syria Thursday to join 66 already there.
On the ground, security forces killed five people on Sunday, marking a brutal start to the New Year, the Syrian Observatory for Human Rights watchdog reported.
Among the dead was a seven-year-old boy, the Britain-based watchdog said.
Protesters on Sunday greeted 2012 with fireworks and fresh protests calling for the ouster of President Basharal Assad, while accusing the Arab League observers of not doing enough to end his regime's brutal crackdown.
On Sunday, an Arab League advisory body called for the immediate withdrawal of the monitors saying their presence in Syria was having no effect on the government's deadly crackdown on dissent.
Arab Parliament speaker Salemal Diqbassi urged Arab League chief Nabilal Arabi to "immediately pull out the Arab observers, considering the continued killing of innocent civilians by the Syrian regime."
The Arab Parliament is an 88-member advisory committee made up of lawmakers from each of the League's 22 member nations.
Damascus's actions are "a clear violation of the Arab League protocol which is to protect the Syrian people," Diqbassi said in a statement.
"We are seeing an increase in violence, more people are being killed including children ... and all this in the presence of Arab League monitors, which has angered the Arab people," he said.
The Local Coordination Committees network of activists echoed the disenchantment with the observers, saying they were not doing enough to protect civilians in flashpoints, namely the Damascus suburb of Daraya.
Daraya residents on Sunday turned out in large numbers on the streets to welcome observers when they heard news of their arrival in their district but "were met with tear gas, live ammunition, brutal attacks," the LCC said.
The Observatory reported late Sunday that more than 20 demonstrators were wounded when security forces fired on protesters in Daraya when they raised an opposition "independence flag."
"Daraya will not break and will not back down... (and) calls on the Arab League observers to fulfill their duties and restore their credibility which was shaken after their absence today in the town squares," the LCC said.
In a statement it urged the monitors to witness repression by "the tyrannical regime's security forces" accusing them of abducting a wounded activist, Mohamed Anwaral Dabbas, from his hospital bed.
"We hope for their presence and testimony, as dictated first by their conscience, and second by their sworn duty," the LCC added.
The Arab League has declined so far to comment on the mission but its Syria operations chief Adnanal Khodeir said on Sunday that more observers will be dispatched Thursday to Syria.
"Around 20 more observers will head to Damascus from Saudi Arabia, Bahrain and Tunisia," Khodeir said.
The monitors are on a month-long mission that kicked off December 26.
Syria agreed to allow the deployment of observers as part of a deal calling for the withdrawal of the military from residential districts, a halt to violence against civilians and the release of detainees.
But the mission has hit snags and triggered controversy.
Mission chief General Mohammed Ahmed Mustafaal Dabi has disputed a YouTube video footage showing an Arab monitor accusing Syrian authorities of posting snipers on rooftops and demanded their removal.
Dabi said the remarks were hypothetical.
A veteran Sudanese military intelligence officer, Dabi is a controversial figure because he served under Sudan's President Omaral Bashir, who is wanted by the International Criminal Court for alleged war crimes.
According to the LCC, a total of 5,862 people were killed in the regime's crackdown last year, including "321 male children, 74 female children and 146 women."
United Nations estimates in early December put the death toll at more than 5,000.
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It's doubtful whether the Arab League should be taken seriously. The leader of the monitors, Sudan's General Mustafa al-Dabi had been accused of committing war crimes in Darfur in the 1990s. The Amnesty International had spoken out against al-Dabi's participation, as it would risk undermining the League's efforts and seriously raise question about the mission's credibility.
The Arabs remain clueless - can you imagine putting someone from Sudan in charge of a mission to investigate charges of human rights abuses.