About 32 people, including 27 civilians, three policemen, and two local paramilitary troopers were injured in the attack.
He called the operation terrorism.
The UN and human rights groups say the volatile situation in Myanmar is putting people's lives at risk. "It is just a destructive terrorist attack".
"Fighting took place since 5am this morning at three places: two military bases in Muse and one near a bridge on the way to Lashio town", TNLA spokesman Major Mai Aik Kyaw told AFP, citing two of the towns in northern Shan where the clashes occurred.
He said the attack was in retaliation for recent attacks on TNLA outposts and for a military offensive against its ally - the Kachin Independence Army - in Kachin state, which occupies the southern tip of the Himalayas.
He challenged the government statistics about the civilian toll from Saturday's violence, saying it was much lower. "We are sorry. But it's hard to say how they were killed during the fighting", said the TNLAA spokesman.
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The TNLA spokesman said he believed some residents had fled over the border.
TNLA forces reportedly attacked a casino run by a militia and a Myanmar army post.
But the effort has been severely hampered by a surge in fighting between Myanmar security forces and an alliance of rebel groups in northeastern Shan and Kachin states.
China on Sunday condemned fighting in Myanmar between government troops and ethnic militants near the Chinese border, that left 19 people dead and caused others to flee into its territory.
Suu Kyi placed the peace bid - an effort to extinguish around two dozen complicated and long-running ethnic conflicts across the country - at the top of her agenda after she was elected to office in landmark 2015 elections.
In addition to Saturday's arrests, at least nine activists across Myanmar were detained, charged or sentenced over the past week for organizing or participating in protests calling for an end to the violence and denial of safe passage to displaced people in Kachin state.