SANAA, Yemen — Yemen’s Shiite rebels and their allies made major advances Wednesday in the southern city of Aden, capturing parts of an upscale neighborhood in fierce combat and seizing men they accused of fighting them.

The gains extended rebel control over the port city, Yemen’s second largest, casting doubt over the effectiveness of a monthlong Saudi-led air campaign intended to drive them out.

Security officials said the Houthi rebels, aided by military forces loyal to former President Ali Abdullah Saleh, had moved up the seaside road in the neighborhood of Khormaksar, taking an area stretching from the Russian Consulate to the Crater business district.

Thousands of civilians fled the fighting as the rebels and their allies searched house by house for suspected adversaries. Eyewitnesses, including activist Maha al-Sayyed, said they pulled some of the men onto the streets and shot them, while warning residents over loudspeakers against harboring fighters.