Issam Basalat, 62, of Telford Road in Edinburgh, is accused of preparation of terrorist acts in relation to his attendance at an alleged meeting of the New IRA at an address at Buninver Road in Omagh, Co Tyrone, on July 19.
David Jordan, 49, of Cappagh Road in Dungannon, Co Tyrone, also appeared at Belfast Magistrates’ Court on Tuesday.
Jordan is accused of belonging to a proscribed organisation between February 8 and July 20, directing a terrorist organisation, and preparation of terrorist acts through attending the same meeting at Buninver Road in Omagh, as well as attending a meeting in Sixmilecross on February 9.
Both men appeared in court remotely by video-link from Musgrave police station.
A PSNI detective chief inspector told the court he believed he could connect the two accused to the charges they face, and agreed he was aware of audio and video evidence in the case.
There was no application for bail.
A defence lawyer for Basalat set out that his client is a GP based in Scotland who previously chaired the Palestinian Society in Scotland and has addressed the Scottish Parliament.
“He has addressed a number of political groups on a number of political issues in an entirely peaceful and democratic way, nor has he come to the attention of the police for any of those activities,” he told the court.
He said his client had been “pestered” to attend and address a public meeting that he believed had an “exclusively political purpose”, while he was in Northern Ireland to obtain a passport for his daughter in Belfast, and went on to claim that his client had been “entrapped” by an MI5 agent.
A defence lawyer for Jordan said issues have been raised around the transcript of some of the evidence.
The PSNI detective chief inspector said police have "extensively looked at all the processes around the acquisition and indeed the timings in relation to the recordings ... we are more than content that the rules of evidence have been complied with and that there are no inaccuracies in relation to the material obtained and indeed that put during interview".
Jordan's defence lawyer also contended that his client had been lured to attend the meetings and brought "under false pretences".
District Judge Fiona Bagnall said on the basis of what she had heard she was "satisfied that the bar has been crossed in order to connect these defendants to the charges which are before the court".
A bail hearing for Basalat is to be heard on September 9.
On Monday, Sharon Jordan, 45, of Cappagh Road in Dungannon, Co Tyrone, Kevin Barry Murphy, 49, of Altowen Park, Coalisland, Co Tyrone, Damien McLaughlin, 44, of Kilmascally Road, Dungannon, Amanda McCabe, 49, of Ailsbury Gardens in Lurgan, Co Armagh, Gary Hayden, 48, of Tyrconnell Street in Londonderry, and Joseph Barr, 32, of Cecilia's Walk in Londonderry, were all remanded in custody on terrorism charges linked to the same police investigation.
On Saturday, Shea Reynolds, 26, of Belvedere Manor in Lurgan, Co Armagh, and Patrick McDaid, 50, of Magowan Park in Londonderry, were remanded in custody.
The 10 co-accused will appear before Belfast Magistrates' Court on September 18.
They were arrested as part of Operation Arbacia, a major PSNI investigation into the dissident republican group which was blamed for the murder of journalist Lyra McKee as she observed a riot in Londonderry last year.
PSNI Assistant Chief Constable Barbara Gray described the operation earlier this week as a "longer term" probe into "every aspect of the activities of the New IRA in its entirety".