South Sudan, one of the world's least developed countries, took three-quarters of Sudan's oil production when it became independent in 2011 but has no refineries and needs to import petrol from Sudan or East African neighbours.
The landlocked nation also needs to export its crude through a Sudanese port but plans to build an alternative pipeline either to Kenya or Djibouti via Ethiopia.
In a first step to end foreign dependency, South Sudan signed a deal last year with a Russian firm to build a mini-refinery with capacity of at least 5,000 barrels a day in Bentiu in Unity state, according to local media reports.
Much of the petrol consumed in the state, which is home to several oilfields, is smuggled in at a premium from neighbouring Sudan.
Kiir also said a second mini refinery, built by U.S. firm Ventech Engineers International in Thangrial Refinery in Upper Nile State, would be launched "very early next year". It will have an initial capacity of 10,000 bpd, officials have said.
He said oil was flowing normally through Sudan despite a threat by Khartoum last month to close two cross-border pipelines unless Juba stopped supporting Sudanese rebels. South Sudan rejects accusations it is backing the rebels.
"Our oil is still flowing at present, we cannot be assured of its continued passage through Sudan," Kiir told a crowd celebrating the country's second independence anniversary.
He said South Sudan would keep talking to Sudan to sort out all conflicts peacefully but he warned oil flows might stop again: "Who knows what will happen tomorrow."
South Sudan shut down its oil output of around 300,000 barrels a day in January 2012 in a row with Sudan over pipeline fees and disputed territory. The neighbours agreed to resume flows in March but distrust runs deep after fighting one of Africa's longest civil wars.
Kiir said austerity measures, imposed after the shutdown, would stay in place until the end of the year. Oil revenues used to make up 98 percent of the budget.
South Sudan's current oil production is unclear. The government sold its first oil cargo last month but officials have not given any production figures in recent weeks.