A tank battalion and armed youths fought with forces belonging to the Majlis (Council) al-Shura, a collection of armed groups including radical militants, in a southern district for much of Friday, army officials said.
As well as the 10 soldiers killed, some 55 were wounded, medics said on Saturday, when much of the city was quiet after gunfire had been heard in several districts the day before.
"The national salvation government confirms ... giving full support, without limits, to Majlis al-Shura troops," it said in a statement posted on the cabinet website. It gave no details.
The Tripoli rulers have not been recognized by the United Nations or world powers. Both sides have fought each other on several fronts, undermining six months of UN meditation efforts which have produced little progress.