In their visits, the 15-member team will urge powerful provincial commanders to work with the government, the BBC reported.
The U.N. Security Council has already voted to expand the more than 5,000-strong NATO-led peacekeeping force beyond the capital, Kabul.
Increasing violence and a rise in drug production are posing a strong challenge to Afghan President Hamid Karzai.
A woman and a child were killed Sunday in clashes between rival militias in the northern Sari Pul province, said Abdul Sabor, a commander under Tajik warlord Gen. Atta Mohammed.
At least five fighters were also killed, two from the Tajik faction, and three from ethnic Uzbek warlord Gen. Abdul Rashid Dostum's forces, the BBC said.
The U.N. team plans to meet both commanders to impress upon them the international support for President Karzai's transitional administration.
More than 300 people, including Taliban fighters, have been killed in violence across the country since the beginning of August.