Chadian police have said anyone wearing a full-face veil will be arrested, a day after a Boko Haram suicide bombing - carried out by an attacker disguised as a women wearing one - left 15 dead.

Saturday's attack at a market in the capital, N'Djamena, also injured 80 others and spread panic across the city. The assailant detonated an explosives belt when he was stopped for security checks at the entrance to the city's main market.

"This attack just confirms that a ban on the full-face veil was justified," national police spokesman Paul Manga said, adding that "it now must be respected more than ever by the entire population".

"Anyone who does not obey the law will be automatically arrested and brought to justice," he warned.

Muslim-majority Chad banned the full-face veil, ramped up security measures and bombed Boko Haram positions in Nigeria last month after the first ever attack by the armed group in its capital.

Security was tightened across the capital on Sunday with police and soldiers deployed in all areas, including intersections, markets and mosques.

Read more: Deadly suicide blast rocks market in Chad capital

Nine of the dead were women traders, and fear still permeated the market on Sunday.

"What was happening elsewhere and what we heard about from media reports is now happening here," said Zenaba, a woman trader in her forties.

"I'm really scared for me and my children," she said.

Boko Haram claimed responsibility on Twitter for the suicide bombing, signing off as "Islamic State, West Africa province" - the fighters' self-styled moniker since pledging allegiance to the Islamic State of Iraq and the Levant group in March.

The conflict has killed at least 15,000 people since 2009 and left more than 1.5 million homeless.

A four-nation coalition of Nigeria, Niger, Chad and Cameroon has reportedly pushed the armed group from captured towns and villages in an operation that began in February.