VANCOUVER — Reporters have been barred from at least one refugee board hearing involving Tamil migrants who arrived on the MV Sun Sea and the Canada Border Services Agency is pushing for even more of the proceedings to be held in secret.

The agency is calling for a full media ban on at least some of the Immigration and Refugee Board hearings after a newspaper inadvertently published the name of one of the migrants last month.

The story identified a man connected with the ship, but did not say he was himself a migrant.

On Monday, the migrant's lawyer asked that reporters be barred from all future proceedings involving his client. The agency did not oppose the application and the refugee board adjudicator granted the request, even though no reporters were present to challenge the ban.

When the migrants first began appearing at their mandatory detention reviews in August, the border agency argued reporters should not be permitted in the hearing room to cover the proceedings.

The request was denied. Instead, a publication ban preventing the reporting of any details that might identify the claimants or their associates was imposed.

On Tuesday, an agency representative asked again for reporters to be barred from a hearing, one involving a woman who's six months pregnant.

"It is our position that the original (publication ban) order is not clear and that perhaps the intent of the order is not clear," Azeem Lalji said at the downtown Vancouver hearing.

Marc Tessler, the refugee board adjudicator hearing the case, rejected the request.

He said the border agency didn't prove why such a ban was necessary, nor had the media been given ample opportunity to respond.

"I don't have enough information about this alleged (publication ban) breach to see how it applies with respect to this person," Tessler said.

Lalji didn't provide specifics on the woman's case and declined to answer questions after the hearing about why barring reporters from the proceedings was necessary.

He suggested reporters get in touch with the agency's media relations department.

A department spokeswoman said the agency wasn't prepared to provide a response Tuesday.

David Poopalapillai, a spokesman for the Canadian Tamil Congress, said his organization opposes full media bans.

"We want the media to be present, then only will the stories come out," he said in an interview. "We want the stories to come out."

The pregnant woman, who arrived in Canada without any identifying documents, was ordered to stay in custody until another detention review hearing later this month.

A border agency representative told the hearing a relative has now sent a copy of her Sri Lankan national identification card, along with her original birth certificate.

As of Tuesday morning, the refugee board had ordered the release of 34 of the migrants.

The MV Sun Sea docked at CFB Esquimalt Aug. 13.

Poopalapillai said he had hoped the process would move a little quicker, though he stressed he's not complaining.

One of the 380 men who was on board the ship has been kept in custody on security grounds.

The rest of the migrants being jailed are being held while the border agency tries to definitively establish their identity.