The separatists' move complicates a long and separate conflict, fought by the coalition and the internationally recognised government, against Huthi rebels who control much of the north.
Yemen's separatists signed a power-sharing deal in Riyadh last November that quelled a battle -- dubbed a "civil war within a civil war" -- for the south that had in August seen them seize control of the second city of Aden.
"Following the surprising announcement of a state of emergency by the Southern Transitional Council, we re-emphasise the need to promptly implement the Riyadh Agreement," the coalition said according to tweets from the official Saudi Press Agency.
"The Coalition demands an end to any escalatory actions and calls for return to the Agreement by the participating parties."
The STC, which is backed by key coalition partner the United Arab Emirates, on Sunday declared self-rule in southern Yemen, accusing the government of failing to perform its duties and of "conspiring" against the southern cause.
The government has condemned the move and said the separatists -- who have long agitated for independence in the south -- would be responsible for the "catastrophic and dangerous" outcome.
The breakdown between the one-time allies comes as the coalition has extended a unilateral ceasefire aimed at fending off the coronavirus pandemic -- an olive branch rejected by the Huthis.
Compounding the country's troubles, at least 21 people were killed in flash flooding this month, with Aden's streets submerged and homes destroyed.
The United Nations said Sunday that more than 100,000 people across Yemen have been affected by the torrential rains which had damaged roads, bridges and the electricity grid, and contaminated water supplies.
"Countless families have lost everything," Lise Grande, the UN's Humanitarian Coordinator for Yemen, said in statement.
"The solution is clear. The parties to the conflict need to find the courage to stop fighting and start negotiating."
- 'Return to the agreement' -
The Riyadh pact on power-sharing for the south had been hailed as averting the complete break-up of the country, but with a lack of implementation, observers have said it is effectively defunct.
Cracks emerged soon after it was signed, with complaints over food shortages in the south, a sharp depreciation of the currency and a lack of funds to pay public sector employees.
"We in (Saudi Arabia) and UAE strongly believe that the internationally backed Riyadh agreement has guaranteed an opportunity for the brotherly Yemeni people to live in peace," Saudi Minister of State for Foreign Affairs Adel al-Jubeir said in a tweet.
"We reject any hostilities that will jeopardise the safety and stability of Yemen," he said.
While the government and the STC are technically allies in the long war against the Huthis, the secessionists believe the south should be an independent state -- as it was before unification in 1990.
On Sunday Aden residents reported heavy deployments of STC forces in the city and a separatist source told AFP they had set up checkpoints "at all government facilities, including the central bank and port of Aden".
"But with this declaration, it will become responsible for the administrative side in the provisional capital that has witnessed an unprecedented decline lately" in the provision of services and economic performance, he told AFP.