Hadi's loyalists made advances amid heavy fighting in the southwestern province surrounding the city which killed around 45 fighters from both sides on Monday, medical sources said.
"Twenty-five pro-Hadi fighters were killed in an ambush laid for them by Houthi and Saleh forces at the Bab al-Mandeb, and 20 Houthi fighters were killed in fighting and coalition air strikes," a medic told Reuters by telephone from Taiz, adding that a family of 8 were killed in an air strike on the city.
Residents said Arab warplanes had bombed Houthi militia targets in the city dozens of times on Tuesday.
At least 5,700 Yemenis have been killed during seven months in a civil war that has pitted supporters of the exiled government, backed by a Saudi-led Arab coalition, against forces loyal to former president Ali Abdullah Saleh and Houthi militia allied to Iran.
It was not immediately clear how long Hadi would stay in the country, his second return to Aden since the Saudi-led coalition retook the port city in July, or whether his visit would herald the permanent return of his exiled administration from the Saudi capital Riyadh.
Mukhtar al-Rahbi, an official in Yemen's presidency, said Hadi had arrived in Aden to oversee the campaign to retake Taiz, which has been battered by fighting. Medics in the city say more than 1,600 people have died there.
"He will also meet with military officials to assess the security situation and to oversee the merging of the resistance forces into the army and security forces," al-Rahbi said.
The coalition has made some progress on the battlefield and took control of Aden in July, but the Houthis still retain control of much of Yemen, despite almost daily air bombardment.