The clashes between Mr Saleh's supporters and the Houthis underscore the complex situation in Yemen, one of the poorest countries in the Middle East, where a proxy war between the Iran-aligned Houthis and the Saudi-backed Mr Hadi has caused one of the worst humanitarian catastrophes in recent times.
The United Nations has warned that the country faces mass starvation unless the Saudi-led coalition allows more food aid to enter the impoverished country.
Houthis and Saleh loyalists jointly overran Sanaa and much of the country in 2014, forcing the internationally recognized government of President Abd Rabbuh Mansour Hadi to flee to Saudi Arabia.
"I call on our brothers in neighboring countries.to stop their aggression and lift the blockade", he said, "and we will turn the page". The rally came after late-night mediation attempts between Saleh and the rebels failed to reconcile both sides, sources said.
Pointing to global law, Lowcock said, "Wars have rules, and they need to be complied with".
There was no immediate word on casualties. In a televised interview, Salah also called for resuming relations with Saudi Arabia, if the Saudi-led coalition lifts its blockade of Yemeni ports and air facilities.
Tillerson urges China to curb oil supply to N
North Korea has been accelerating its threat to the United States and to the globe with recent missile tests. France is expressing its solidarity with Japan and South Korea in the face of this threat...
The statement was issued after a meeting between Hadi and his advisers to form a broad national alliance in the face of the militias Houthi.
The Saudi-led coalition - which has fought Saleh and the Houthi rebels since 2015 - last month imposed a total blockade on the impoverished country after a rebel missile was shot down near Riyadh.
The Houthis accused Mr Saleh of betrayal, and vowed to keep up the fight against the Saudi-led coalition.
"It is not unusual or surprising that Saleh turns back on a partnership he never believed in", the group's political bureau said in a statement.
For his part, Houthi leader Abdel Malek al-Houthi called on Saleh to end what he called "the sectarian strife" that he has instigated, and threatened to take action against his supporters militarily if he does not.
Saleh and the Iran-backed Huthis, also known as Ansar Allah, have accused each other of inciting Wednesday's unrest.
Yemen's war has killed more than 10,000 people since 2015, displaced more than two million people, caused a cholera outbreak infecting almost one million people and led the country on the brink of starvation.