A teenager in Northern Ireland has been charged with making a social media death threat against Jacinda Ardern after the Christchurch terror attacks.

Matthew Burns is alleged to have posted an image of gun fitted with a silencer to the Prime Minister, along with the caption "you're next" on March 20, five days after 50 people were killed as they worshipped at two mosques.

Ardern has received worldwide attention and praise for her response to the terror attacks.

Burns, who is from Newtownhamilton, 75km south of Belfast, was also charged with sending a message of menacing character to London Mayor Sadiq Khan in December.

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The 19-year-old was arrested and charged on Thursday after the Police Service of Northern Ireland's Cyber Crime Unit traced the online threats to the business student's IP address.

Newry Magistrates Court heard a threat was made from the same account to Khan.

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.

During police interviews, Burns confessed to posting the threats, the investigating officer said.

Burns also told detectives during interviews that his political view was far right and that he was against minority groups, including immigrants and members of the LGBT community.

"He agreed with the sentiments contained in the posts. He has antipathy towards minority communities."

District Judge Mark McGarrity refused an application for reporting restrictions in the case.

"Mr Burns, the police will be watching you," Judge McGarrity said.

The defendant was released on £500 (NZ$965) bail with a £1000 (NZ$1931) cash surety on the condition that he had no internet connection and adhered to a 7pm-7am curfew.

The case was adjourned to May 8.