Matthew Burns is alleged to have posted an image of gun fitted with a silencer to Ardern, along with the caption "you're next" on March 20, five days after the carnage at two mosques, the New Zealand Herald reported on Saturday.
Burns, a resident of Newtownhamilton, 75 km south of Belfast, was also charged with "sending a message of menacing character" to London Mayor Sadiq Khan in December. Newry Magistrates Court heard a threat to Khan was made from the same account.
The investigating officer said further posts of racist, xenophobic, sectarian and homophobic nature were also found to have been sent from the same IP address.
Burns confessed to posting the threats, according to the officer. He told detectives his political view was far right and that he was against minority groups, including immigrants and members of the LGBT community.
The defendant was later released on 500 pound bail with a 1,000 pound cash surety on the condition that he will not have an Internet connection and will adhere to a 7 p.m.-7 a.m. curfew.
The case was adjourned to May 8.
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