Saudi forces arrived on Wednesday in Shaqra and Sheikh Salem, two flashpoints in southern Yemen's Abyan province, to monitor the truce that was announced only on Monday, military sources said.
"Observers have begun to be deployed on the ground to monitor the comprehensive ceasefire and separation of forces," the coalition said Wednesday, according to Saudi government TV station Al-Ekhbariya.
"Both parties have affirmed their commitment to respect the ceasefire, to de-escalate and normalise the situation, and to implement the Riyadh Agreement," it added.
The Riyadh Agreement, which was struck last November but quickly became defunct, is a power-sharing deal for the south, where a separatist insurgency has revived long-standing independence ambitions.
The conflict has emerged as a second front in a country already split by a five-year war between Houthi rebels, who control the capital Sanaa and the north, and the government, which was forced south to the interim capital of Aden.
Shaqra and Sheikh Salem were the scene of clashes between government troops and southern separatists that raged through Tuesday and into the night, the sources said.
"Our forces in Abyan suffered a violent attack by the invading forces a few hours after the ceasefire came into effect," Nazar Haitham, spokesman for the separatists' Southern Transitional Council (STC), told AFP.
"It is an irresponsible act of the government, which says it is bound by the ceasefire but does not respect it on the ground," he said.
The Yemeni government has not made any statement on the accounts of clashes.
A collapse of the ceasefire would again complicate efforts by the government, backed by the Saudi-led coalition, to repel the Iran-backed Houthi rebels.
The southern separatists and the government are technically allies in the fight against the Houthi rebels, but the rift between them represents a damaging "war within a war" in the Arabian Peninsula's poorest country.
The STC declared self-rule on April 26, accusing the government of failing to carry out its duties.
The STC has made a series of military gains, the latest on Saturday when it seized control of the island of Socotra off the southern coast of Aden - located near strategic shipping lanes and famed for its biodiversity.
The separatists and the government are due to hold further talks in Saudi Arabia to discuss the truce, coalition spokesman Turki al-Maliki said on Monday.
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