Dozens of the fugitives' relatives and friends have been detained for questioning, said the official, who did not wish to be identified.
"The combing operation is taking place in areas seen as strongholds of extremist groups," the official said. "There have been arrests of kin and friends."
The official said the main search effort was in the Abyan province in the south, but also the capital Sanaa as well as remote areas.
On Sunday, the Interpol issued a global security alert over the escape of the militants who tunnelled their way out of a jail in Sanaa, calling them a "danger to all countries".
The 13 militants were among 23 inmates who escaped in a major embarrassment for Yemen, which has cracked down on militants in the ancestral land of Osama bin Laden and positioned itself as an ally of the United States.
They included Jamal Badawi, mastermind of the bombing of the US destroyer Cole in the Yemeni port of Aden in October 2000, which killed 17 US sailors. He was originally sentenced to death, but this was later commuted to 15 years in prison.
Another prominent escapee was Fawaz al-Rabe'ie, sentenced to death as leader of the group convicted of bombing the French oil tanker Limburg off the Yemeni coast in 2002, killing one crewman.
A Yemeni security source has said authorities discovered the escape on Friday, but it was believed the prisoners had fled Thursday night and were definitely aided by more than one accomplice on the outside because the tunnel was believed to have been dug from the mosque to the prison.
The tunnel entry was in the women's section of the mosque, less frequented than the male section because women mainly pray at home.