The claim could not immediately be verified and activists near the capital Damascus denied troops were leaving their area. They said the day regime forces withdraw from streets, Syria will witness massive protests that will overthrow the government.
"Forces began withdrawing to outside calm cities and are returning to their bases, while in tense areas, they are pulling out to the outskirts," the government official said in Damascus without saying when the withdrawal began. He spoke on condition of anonymity because he was not authorized to talk to the media.
President Bashar Assad agreed just days ago to an April 10 deadline to implement international envoy Kofi Annan's truce plan. It requires regime forces to withdraw from towns and cities and observe a cease-fire. Rebel fighters are to immediately follow by ceasing violence.
Khaled al-Omar, an activist in the Damascus suburb of Saqba, denied that any withdrawal was underway in his area.
"This is impossible. I can see a checkpoint from my window," he said via Skype, adding the regime forces were still in the main square.
Earlier in the day, opposition activists charged that the regime was racing to crush opponents ahead of the cease-fire deadline by carrying out intense raids, arrests and shelling Tuesday.
Opposition activists have blasted Annan's plan as too little, too late and are particularly angry that it does not call for Assad to leave power -- the central demand of the uprising. They suspect Assad will manipulate the plan and use it to stall for time while his forces continue to crack down.
"He thinks he can win more time to take control of all Syrian cities," activist Adel al-Omari said by phone from the southern town of Dael, where regime forces have been torching activists' homes since they raided Monday. "This won't happen, because as soon as he withdraws his tanks from the cities, the people will come out and push to topple the regime."
Western leaders have cautiously accepted the April 10 deadline while pointing out that Assad has broken previous promises and insisting the regime must be judged by its actions.
Also Tuesday, Amnesty International said people are still being arrested across Syria, including 13 students who were beaten at their school in the Damascus suburb of Daraya.
The organization said it received the names of 232 individuals, including 17 children, who were reported to have been killed since Syria agreed to the plan on March 27.
"The evidence shows that Assad's supposed agreement to the Annan plan is having no impact on the ground," said Suzanne Nossel, executive director of Amnesty International USA.
She said the government must released thousands of prisoners, stop arrests and halt violence "Otherwise, the only conclusion we can draw is that Syria has made empty promises once more," Nossel said.
Russia's Foreign Ministry said Tuesday that Syria had informed its close ally Moscow that it has started implementing the plan. The ministry's statement did not say which troops -- if any -- had been withdrawn or provide further details. It called on rebel forces to follow suit.
The Syrian government has not commented publicly on the April 10 deadline. It has accepted other peace plans in recent months only to ignore them on the ground. An Arab League effort that included sending in monitors to promote a cease-fire collapsed in violence in November.
It also remains unclear whether rebel forces fighting government troops under the banner of the Free Syrian Army would respect a cease-fire. Dozens of local militias in different parts of the country have only loose links to each other and to their official leadership in Turkey.
One activist in the central Homs region said Tuesday that the area's biggest rebel group, the Farouq Brigade, would cease its attacks on government targets if the government stopped shelling towns and cities.
"They will continue to resist until they see that there is a positive step from the regime," Mahmoud Orabi said via Skype from the town of Qusair. "If the regime withdraws and carries out the plan, the Free Army will respect it, too."
Activists said Syrian forces shelled rebellious neighborhoods in the central city of Homs and the nearby towns Qusair and Rastan Tuesday and carried out raid and arrest campaigns elsewhere.
The Britain-based Syrian Observatory for Human Rights said at least two civilians were killed in clashes between rebels and government forces that stormed the town of Taftanaz and torched a number of homes.
Gunmen in the northern city of Aleppo attacked the home of the head of military institutions late Monday and killed two guards, the groups said.
Another activist group, the Local Coordination Committees, said at least 13 people were killed nationwide, six of them in Homs province and 5 in the raid of Taftanaz.
The activists' claims could not be independently verified. The Syrian government rarely comment on specific incidents and has barred most media from working in the country.
Relentless government shelling of rebellious areas and frequent clashes with rebels have taken a high toll on Syria's civilians, and the International Committee of the Red Cross pressed Syria on Tuesday to give aid workers access to embattled areas.
ICRC president Jakob Kellenberger met with officials from Syria's foreign, interior and health ministries, as well as the head of the local Red Cross branch. He said before his visit that he would appeal for greater access to the sick, wounded and displaced and press for a two-hour daily halt to the fighting to allow aid in.
Aji reported from Damascus.