The Shiite Huthi militia, backed by troops allied to former president Ali Abdullah Saleh, clashed with forces loyal to Hadi in at least two southern provinces yesterday as they pushed on Aden, sources said.
In another southern city, Taez, the militia shot dead five demonstrators as protests intensified against the Huthi presence, in what Amnesty International denounced as a "shocking disregard for human life".
The militiamen have seized large parts of Yemen and, in recent days, have been moving towards Aden, where Hadi fled after escaping house arrest in the capital Sanaa last month.
The UN Security Council, Western countries and Gulf Arab monarchies have backed Hadi as the country's legitimate ruler.
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Yesterday, he called for the UN to go further and painted a dark picture of the crisis, raising concerns that Al-Qaeda will "seize the current instability to spark further chaos".
He also referred in a letter to the Security Council to an unspecified "missile capability looted from the legitimate authority", and asked the body to take control of the missiles.
Diplomats on the council said no new meeting has been planned at this time.
Tuesday's clashes came after the Huthis seized the airport and a nearby military base Sunday in Taez, 110 miles north of Aden and seen as a strategic entry point to Hadi's southern refuge.
The Huthis have been increasingly joined in the fight by troops loyal to Saleh, who resigned in 2012 following nationwide protests but has been accused of allying with the Shiite militia as he seeks to regain influence.
Dozens of tanks belonging to the 133rd Brigade, also loyal to Saleh, were sent to Qatabah, military sources and witnesses said.
These troops clashed with Hadi supporters in the surrounding province and took control of the headquarters of the local government in the provincial capital Daleh, military and security sources said.
Clashes also erupted in the province of Lahj, just north of Aden, where forces loyal to Hadi had deployed in anticipation of an attack.