A senior Orangeman said Northern Ireland Secretary Sir Chris Bryant has been “left in no doubt” the law must be applied to allow their parade in Drumcree to proceed.

The latest round of talks over the parading stand-off, which has now entered a fourth day, are under way.

Sir Chris has been hosting delegations from the Orange Order and Garvaghy Road residents at Hillsborough Castle in Co Down.

Police Service of Northern Ireland Chief Constable Jon Boutcher has also been taking part in meetings around the stand-off, described as “in the backdrop and support” of the ongoing discussions with Sir Chris.

In a statement on Wednesday afternoon, Mr Boutcher said police had “once again become the shock absorber of our society”.

He also warned: “People shouting at me has absolutely no effect on my judgment and they would do well to learn that.

“My overriding responsibility is to keep people safe.”

Orangemen have been waiting since Sunday to take part in their parade down the mainly nationalist Garvaghy Road in Portadown.

They have tried on several occasions to begin the parade, but have been prevented by police.

The PSNI has said a protest in opposition to the parade on the Garvaghy Road is unlawful but using force to move protesters risks people getting “seriously hurt”.

An Orange Order delegation was the first to arrive at Hillsborough Castle for talks with Sir Chris on Wednesday.

The group was made up of Portadown District Master Nigel Dawson, deputy District Grand Master Alastair Power and their legal adviser Jamie Bryson.

They left around two hours later.

Mr Dawson said: “We have just concluded another meeting with the Secretary of State.

“Obviously the contents of these meetings remain confidential.

“However, the Secretary of State has been left in no doubt that our continued position is that he must, and the chief constable, must apply the law in relation to the positive determination issued by the Parades Commission and reinforced by the High Court.”

A delegation of residents from the Garvaghy Road are still meeting with the Secretary of State.

The group was led by Breandán Mac Cionnaith, from the Garvaghy Road Residents Coalition.

Asked what his message for the Northern Ireland Secretary is, Mr Mac Cionnaith said: “I think you know that.”

The two groups are not meeting face to face, but instead held separate meetings with Sir Chris in the Edenderry Room in the castle.

While both groups were accompanied by legal advisers, they are not taking part directly in the talks.

The dispute is now set to return to the courts, with lawyers for the Garvaghy Road residents having launched a fresh legal bid to try to prevent the controversial Drumcree march from going ahead.

Their latest legal challenge, which argues the Parades Commission “materially misdirected itself” on the police assessment of the potential for disorder, is set to be heard on Friday.

Efforts to call off the parade were brought to Government Buildings in Dublin on Tuesday where Sinn Féin leader Mary Lou McDonald and deputy leader Michelle O’Neill, Northern Ireland’s First Minister, met Taoiseach Micheál Martin and Tánaiste Simon Harris.

Ms O’Neill has faced criticism from unionists after she and senior colleagues were among a large crowd that blockaded the road on Sunday to prevent the parade from passing the route.

On Wednesday morning, TUV MLA Timothy Gaston said he had tabled exclusion motions at the Northern Ireland Assembly for Ms O’Neill and other Sinn Féin ministers in the Stormont Executive.

He claimed they “no longer enjoy the confidence of the Assembly” after “participating in the unlawful protest on the Garvaghy Road on September 27 which prevented a permitted parade from proceeding”.

He is calling for them to be excluded from holding office as a minister or junior minister for a period of 12 months.

Under parading laws in Northern Ireland, protests must be notified to, and approved by, the Parades Commission adjudication body.

The Drumcree parading dispute, which was associated with violent disorder during the Troubles, has been reignited after the Parades Commission granted permission for a limited parade down the Garvaghy Road for the first time in almost 30 years.

At the height of the blockade on Sunday, more than 1,000 people congregated on the road to prevent the parade from the Drumcree Church from passing along the route.

The Drumcree parade down the Garvaghy Road had previously been banned since 1998.

On Friday, the commission reversed its long-running determination and granted permission for the parade – a decision welcomed by unionist parties and met with outrage from nationalist and republican parties.

Permission was granted for a parade subject to strict restrictions, including a limit of 35 participants and an 8am start time.