Foreign Minister Mohammed al Hadhrami said the Southern Transitional Council had refused calls from the government and the international community to reverse its declaration of self-rule.
Yemen's government forces will confront an "armed rebellion" by separatists in the south, the government said on Tuesday, adding that the group had refused to de-escalate the situation after declaring self-rule last month.
On April 25, the Southern Transitional Council (STC) declared self-rule in Aden and nearby areas, threatening to renew a conflict with the Saudi-backed government, its nominal ally in a coalition fighting Yemen's Houthi group.
Foreign Minister Mohammed al Hadhrami said the STC had refused calls from the government and the international community to reverse its declaration.
The army will do "everything necessary to preserve the state, its institutions, and the safety of its citizens against (the STC)", he added.
Hadhrami urged the group to implement the Riyadh pact, a power-sharing deal brokered by Saudi Arabia in November to defuse tension after the STC briefly took over Aden in August.
Both sides have accused each other of destabilising military actions in the south, in particular in the province of Abyan.
In a speech on Monday, STC leader Aidarous al Zubaidi called for southern forces to be "ready" urging people in the region to "defend their national gains".
Aden is the interim seat of the government ousted in late 2014 from power in the capital, Sanaa, by the Iran-aligned Houthis.
It has reported most of the country's 58 coronavirus infections and the government said the political issues with the STC were hampering the virus fight, while the STC has accused the government of incompetence and corruption.
The five-year war has shattered Yemen's health system and pushed millions to the brink of famine.
The World Health Organization says Yemen is suffering full-blown transmission of the virus, among a population with some of the lowest levels of immunity to disease among nations.
The Saudi-led coalition has announced a unilateral truce, prompted by a UN plea to focus on the virus pandemic, but the Houthis have not accepted it and violence has continued.
The UN is trying to convene virtual talks on the truce, coordinated virus efforts and confidence-building steps to restart talks to end the war.