Six protesters reportedly died when troops opened fire to disperse a huge crowd urging the monitors to speak out.
The UN says more than 5,000 have been killed in the nine-month-old uprising.
The Syrian government – which says it is fighting “armed terrorist gangs” – says 2,000 members of the security forces have lost their lives.
Casualty figures and other information are hard to verify from Syria as most foreign media are preventing from reporting freely.
The BBC’s Jim Muir in neighbouring Lebanon says the first day of the Arab observer mission brought several clear messages.
Syrian security forces, which had by multiple accounts been pounding several residential areas in Homs with artillery, eased off on Monday before the observers arrived and pulled some tanks off the streets.
But when tens of thousands of protesters took to the streets, tear gas and live fire were used to disperse them, despite the fact that under the Arab League peace initiative, all military forces are supposed to be withdrawn and peaceful demonstrations permitted.
Video footage posted on the internet showed angry residents in the flashpoint district of Baba Amr surrounding the monitors and pointing to pools of blood as gunfire rang out in the background.
Activists said security forces killed at least 16 people across Syria on Tuesday, including six in Homs. One group, the Local Co-ordination Committees, put the death toll at 42, including 17 in Homs and seven in the nearby city of Hama.
Despite the reported violence, Gen Dabi told Reuters on Wednesday morning: “The situation seemed reassuring so far.”
“There were some places where the situation was not good,” he said. “But there wasn’t anything frightening, at least while we were there. Things were calm and there were no clashes.”
“We did not see tanks but we did see some armoured vehicles.”
“But remember this was only the first day and it will need investigation. We have 20 people who will be there for a long time,” Gen Dabi added.
Gen Dabi also told the AFP news agency that by dawn on Thursday, observers would be deployed in three other centres of the uprising – Hama, the north-western province of Idlib and the southern province of Deraa. They will also fan out up to 80km (50 miles) around Damascus.
Human rights groups have criticised the appointment of Gen Dabi, saying that it is impossible to imagine someone who has held senior Sudanese military and government posts, including in the Darfur region, ever recommending strong action against Syrian President Bashar al-Assad.
The Arab League says Gen Dabi has vital military and diplomatic expertise.
Meanwhile, Human Rights Watch accused the Syrian authorities of hiding hundreds of detainees, who should be released under the peace plan, in military installations, which the observers are not permitted to visit.
A Syrian security officer in Homs told the New York-based group that after the government signed the Arab League protocol authorising the observer mission, between 400 and 500 prisoners were moved out of his facility to other places of detention, including at a nearby missile factory.
Syria’s top international ally, Russia, has urged the regime to co-operate fully with the observers and allow them as much freedom of access as possible.
Our correspondent says that if Syria’s government loosens its iron grip, as the Arab League peace plan insists it should, whole towns and cities will fall out of its control.
That is why, he adds, the opposition is convinced that the government is just going through the motions of co-operating with the Arab League, stringing the observers along and making some cosmetic changes on the surface, while trying to leave the basic situation unaltered.