Sogavare said as a result of the second positive test other planned repatriation flights from the Philippines were being suspended.
However, he said health officials advised that the virus was still being contained in quarantine.
"So my fellow citizens my message to you all today is the risk of community spread of this virus is still low and therefore we will not implement an immediate general lockdown," he said.
Sogavare apologised to students still stranded in the Philippines, promising that the government was still committed to bringing them home as soon as possible.