The average price of the top Kenyan tea grade edged higher to $3.83 per kg at this week's auction from $3.81 per kg at the previous sale, although many lower quality teas remained unsold, brokers said.
Best BP1s sold for $3.90-$3.76 compared with $3.90-$3.72 at last week's sale.
Africa Tea Brokers (ATB) said in a regular market report that 38 percent of the 7,445,382 kg (118,193 packages) on offer were not bought, the highest ever number of unsold teas in recent times.
Last week, 22 percent of the tea on offer went unsold while and all but 5 percent of the packages were snapped up at the previous sale.
ATB said there was less interest at this week's auction from Egyptian, Pakistani and British buyers -- all usually significant buyers of Kenyan tea at the weekly auction in the port city of Mombasa.
Somali buyers, who typically go for lower quality teas, were also less active.
Best Pekoe Fanning Ones fetched $3.44-$3.68 per kg, down from $4.02-$3.59 per kg previously.
Kenya is the world's largest exporter of black tea and last year it earned $1.2 billion, making it the country's top hard currency earner ahead of horticulture exports.
The weekly auction also handles tea from neighbouring producers such as Tanzania and Burundi.