Mr Singh said he planned to lodge a complaint with the Human Rights Commission and Ombudsman.
Colonel Tevita Mara, who is in exile in Tonga, is also alleged to be part of the assassination plot, but he denied any knowledge of it.
Mr Key said Colonel Mara was banned from visiting New Zealand and could visit only if granted a permit.
"Every time he comes to New Zealand we have to grant him a exemption to a ban - whether we will grant him a future exemption is a matter that we'd have to take some advice on at the time," he said.
He indicated the Government had already been in touch with the military regime in Fiji over the alleged assination plot.
"When the Government believes it needs to communicate with other interested parties it does so."
Fiji has been under the control of a military regime since Commodore Bainimarama seized power in a coup in 2006.