The resignation is with effect from February 17.
He is a member of the opposition faction headed by Mr Taban Deng Gai, Africa Review reports.
Gen. Lam said he was unhappy with the direction President Kiir was leading the country.
According to him, President Kiir is running a national unity government, which Lam has described as partial.
“Without wasting much of your time, ladies and gentlemen of the press, I Lt. General Gabriel Duop Lam, the National Minister of Labour, Public Service and Human Resource Development in the republic of South Sudan, with sound mind and excellent rule of reasoning, do hereby officially resign.
“I resign from the position of being the minister in the so called Government of National Unity with effect from February 17.”
He circulated copies of the letter of resignation to the media in Juba on Friday.
Gen Duop also declared allegiance to the rebel leader, Dr Riek Machar, who was leading an armed struggle against President Kiir.
Last week, a top army commander, Gen. Thomas Cirilo, also cut ties with President Kiir and quit military service.
News Agency of Nigeria (NAN) reports that South Sudan peace remains at stake despite pledges from President Kiir to enforce stability across the country.
Over a million South Sudanese have become refugees since the conflict erupted in 2013. Thousands more have lost their lives.
The security situation remains tense in Eastern and Central Equatoria and in Upper Nile’s Malakal and Unity areas.
Posted by Juliet Ekwebelam