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The proclamation was read by the Norroy and Ulster King of Arms Robert Noel
The Accession Proclamation has been read at Hillsborough Castle in County Down, at the same time as ceremonies in Edinburgh and Cardiff.
The reading of the Principal Proclamation of the new King, Charles III, took place at St James's Palace in the City of London on Saturday.
King Charles is due to make his first visit to Belfast as monarch on Tuesday.
Prime Minister Liz Truss is expected to accompany the King, along with Camilla, the Queen Consort.
Charles became King following the death of his mother, Her Majesty Queen Elizabeth II, on Thursday and an historic meeting at St James's Palace formally confirmed his role on Saturday.
As part of a UK tour, the King and Camilla will arrive in Belfast on Tuesday before travelling to Hillsborough Castle.
The Queen first visited Northern Ireland just after the end of World War Two in 1945, when she was Princess Elizabeth.
Scott Carson, the Mayor of Lisburn and Castlereagh City Council, said the people of Hillsborough were eagerly awaiting the arrival of the King.
"I think there is a great sense of anticipation and positivity already in the air," he said.
"The Royal family and especially King Charles, have fond memories of Royal Hillsborough and Hillsborough Castle and he has enjoyed spending time here and I look forward to seeing him visit shortly and I know the people within Royal Hillsborough and the whole borough and across Northern Ireland are also eagerly awaiting that as well."
During Tuesday's visit, King Charles will meet the new Secretary of State for Northern Ireland, Chris Heaton-Harris, as well as local party leaders.
He is to receive a message of condolence led by the Speaker of the Northern Ireland Assembly.
The King and Queen Consort will then meet leaders from all the major faiths in Northern Ireland before a service of prayer and reflection at St Anne's Cathedral in Belfast.
In the midst of very heavy rain, the proclamation ceremony went ahead and in some ways it was quite symbolic as the Royal Family has come here in good times and in bad, in good weather and in bad.
It is a day to look forward as well as back.
It is a significant day here at Hillsborough Castle and another significant day is coming on Tuesday when King Charles III is due to make his first visit to Northern Ireland as monarch.
He came here 39 times as Prince of Wales.
His 40th trip to Northern Ireland will be as King Charles III and one of the places he will visit is Hillsborough Castle, the royal residence.
On Saturday, a gun salute at Hillsborough Castle marked the Principal Proclamation of King Charles.
At Hillsborough Castle on Sunday, the Accession Proclamation was read at 12:00 BST by the Norroy and Ulster King of Arms Robert Noel in front of an audience of dignitaries and members of the public.
Norroy and Ulster King of Arms is one of the three senior officers of arms at the College of Arms in London, the heraldic authority for England, Wales, Northern Ireland and parts of the Commonwealth.
The proclamation event featured military in full ceremonial dress, a bugler and a 21-gun salute.
Sinn Féin said it would not be represented at the reading of the Accession Proclamation at Hillsborough Castle.
However, the party said it acknowledged "the positive role the Queen played in advancing peace and reconciliation" and said that in recognition of this it would attend a number of events during the period of national mourning.
The Social Democratic and Labour Party (SDLP)'s councillor Simon Lee was in attendance.
The party said it had "not been prescriptive or prohibitive with its public representatives about attending events related to the death of Queen Elizabeth II".
"It is for each representative to decide which events they attend, taking into account their personal circumstances and conscience.
"The SDLP Leader will attend a number of events in London this week and it is the intention of senior SDLP representatives to attend the motion of condolence and service of thanksgiving in Belfast on Tuesday."
Following the formal regional proclamation at Hillsborough Castle, the document was read in several council areas by lord lieutenants or sheriffs.
By Niall McCracken, BBC News NI in Edinburgh
People from Northern Ireland are among thousands lining streets in the centre of Edinburgh as the Queen's funeral cortege makes its way to the Scottish capital from Balmoral Castle.
Grace Cubitt, who is from Northern Ireland but has lived in Edinburgh for five years, said she had come on behalf of her family.
"We got here early, so we're just going to hold our spot for the next few hours so that we can pay our respects," she said.
The procession is due to enter from the west of the city, skirt by Edinburgh Castle and travel down the Royal Mile to the Palace of Holyroodhouse by about 16:00.
Read more here.
At 15:00 BST on Sunday, hundreds of people attended Belfast City Hall for a re-reading of the Accession Proclamation by the High Sheriff of Belfast, Democratic Unionist Party (DUP) councillor John Hussey.
He was in full ceremonial robes as he led the event in the main foyer.
The Lord Lieutenant of the County Borough of Belfast, Dame Fionnula Jay-O'Boyle, was also present.
After the event, council members gathered in the main council chambers for a special meeting to pay tribute to the late Queen.
Shuttle bus services to Royal Hillsborough from the Eikon Centre have resumed following a pause for the proclamation ceremony.
Visitors are being warned parking is restricted and a one-way system is now in operation in the village.
Belfast City Hall will be open until 20:00 BST on Sunday for people who want to sign the books of condolence. The building will also be open Monday to Friday from 09:30 until 20:00 BST.
People have been leaving floral tributes in the Garden of Remembrance which is open 07:00 BST to 20:00 BST daily.
Visitors are being warned of restrictions around Hillsborough Castle during the period of official mourning.
The Orange Order has suspended all planned parades until after the funeral.
Other councils are holding events on Sunday:
The Queen's funeral will be held on Monday 19 September at Westminster Abbey in London.
On Saturday, during the Accession Council, the King approved the day of the Queen's funeral becoming a bank holiday.
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