Northern Ireland saw three decades of sectarian conflict over British rule, known as "The Troubles", that claimed some 3,500 lives.
But the province stands transformed since the Good Friday Agreement was adopted on April 10, 1998.
"However, a small number of people remain determined to cause harm to our communities through acts of politically motivated violence," Heaton-Harris told parliament.
He urged the public to "remain vigilant, but not be alarmed" at the announcement.
It follows a police officer being shot and seriously wounded in front of his son last month, while November saw a failed bomb attack on two officers.
Both attacks have been blamed on a dissident militant group called the "New IRA", which wants reunification with the Republic of Ireland.
The threat level was lowered to "substantial" a year ago -– the first change since 2010.
Chief Constable Simon Byrne, head of the Police Service of Northern Ireland, said the new alteration was "part of an ongoing process of monitoring".
He vowed to "relentlessly pursue those who seek to cause harm and terrorize our communities, and attack my officers and staff".
Heaton-Harris, who insisted there would be "no return to the violence of the past", drew no link to the planned trip by Biden.
The US leader intends to visit both Ireland and Northern Ireland.
It is expected to coincide with the anniversary of the peace deal, which was brokered with US mediation.
The anniversary comes with the territory locked in political paralysis, as pro-UK unionists refuse to re-enter government in objection to a post-Brexit trade deal agreed by London and the European Union.
More extreme militants in the pro-UK camp have issued periodic warnings about the consequences of the agreement, which they argue leaves Northern Ireland at risk of political and economic divorce from Great Britain.
Prime Minister Rishi Sunak defended a recent renegotiation of the elements of the pact, dubbed the Windsor Framework, as he urged the pro-UK Democratic Unionist Party (DUP) to resume power-sharing in Belfast's Stormont assembly.
"I believe the Windsor Framework represents a fantastic foundation for us to move forward and actually just build that brighter future for Northern Ireland which is there for the taking," he told MPs in London.
"The anniversary of the Good Friday Agreement gives us a chance to reflect on the progress we've made, and the opportunities that lie ahead," Sunak added.
DUP leader Jeffrey Donaldson called the ruling by MI5 "bad news".
"I look forward to a day when the threat level is removed, but to get there the community must stand with the police and demonstrate there is no space for terrorism in Northern Ireland in 2023," he said.
Donaldson urged the UK government to make good on a commitment to help fund the hiring of 7,500 extra police officers in the territory.
Northern Ireland's Sinn Fein leader Michelle O'Neill, who is set to become first minister if power-sharing is restored, said there is "no place or space for paramilitary groups".
"They must go," she tweeted.