In an interview with Aljazeera on Thursday, Murad said "the sixth stage of the redeployment of Syrian troops in Lebanon has started on Thursday".
He added that according to the 1989 Taif Accord, all Syrian troops should withdraw to the eastern Bakaa Valley.
"The Lebanese and Syrian leadership have met and decided on the sixth redeployment of the Syrian forces in Lebanon," Murad said.
"They took the decision to start the redeployment in the next few hours. After this redeployment, all the Syrian forces will be in the Bakaa," he said.
Further meetings would take place to "define the number of the troops which will remain in the Bakaa and to define the spots where they will be stationed in that area", he added.
Earlier on Thursday, the Syrian Foreign Ministry announced Syria would withdraw its troops from Lebanon.
Beirut demonstrators called for
the withdrawal of Syrian troops
"The important withdrawals have already been carried out and what will be carried out later will be in agreement with Lebanon based on the Taif Accord," the ministry statement said.
The announcement by Syria, was the first government statement since the international uproar against Damascus over the 14 February assassination of former Lebanese prime minister Rafiq al-Hariri.
Syria has about 14,000 troops in Lebanon and is the main power broker there.
Damascus also said it was keen to cooperate with the United Nations to implement a resolution requiring the state to pull its troops out of Lebanon.
"Syria expresses its keen interest in cooperating with the envoy of the secretary-general of the United Nations to accomplish his mission in the best formula possible," Syrian Deputy Foreign Minister Walid al-Mualim said.
Also on Thursday, Lebanese Prime Minister Umar Karami said a quick Syrian troop withdrawal would destabilise Lebanon.
Karami: Pullout will shake the
stability of the country
Asked about international and domestic calls for an immediate pullout of Syrian troops and security services, he said: "In our opinion, it would shake the stability of the country."
Syrian troops are currently based on high mountains overlooking the coast to the west and the Bakaa to the east, with positions also in northern Lebanon. The bulk of the Syrian garrison - which once numbered 35,000 - has withdrawn from the coast and the lower ground in redeployments since 2000.
US President George Bush and French President Jacques Chirac have this week repeatedly demanded a full Syrian army withdrawal from Lebanon. The United Nations Security Council demanded the same in a resolution last September.
Meanwhile, Israel welcomed the Syrian announcement. Foreign Ministry spokesman Mark Regev said: "Israel supports implementation of UN Security Council [resolution] 1559, which calls for the withdrawal of foreign forces and the disarming of all the militias, including Hizb Allah."
An Israeli official, speaking on condition of anonymity, said Israel would have to study the Syrian declaration to determine if it promised a real change.
Israel withdrew its forces from Lebanon in 2000 after an 18-year war against Hizb Allah. The United Nations drew the border between Israel and Lebanon, but Hizb Allah disputes part of it.
Regev added: "Israel has done its part to implement UN resolutions when we pulled out of Lebanon, and I think now the international community is waiting for Syria to do its part."