Update 1.50pm: The DUP leader has unveiled a large banner hitting out at Sinn Féin on the day Northern Ireland matches Belgium's record of the longest time without a functioning government.
Arlene Foster's party has failed to reach an agreement with Sinn Féin to enter government as the two largest parties.
The dispute centres on issues such as the Irish Language and same sex marriage.
The DUP leader says there is no sign of progress any time soon.
"There is only one problem party and let's call it out - that's Sinn Fein," she said. "And they need to end their boycott here in Northern Ireland.
"I share the frustrations of many today that we don't have a government here taking decisions on education and on health, on infrastructure and on the future of this country itself.
"So it's time to get back into government - long past the time to get back into government."
Mrs Foster repeated her call for government to be restored while a parallel process to resolve outstanding issues is run.
The DUP is deeply frustrated that we have reached 589 days without a government. It’s time for SF to end its boycott of the Assembly. pic.twitter.com/LRZmWM6C5y— Arlene Foster (@DUPleader) August 28, 2018
The UK Government has acknowledged the deep frustration of the public in Northern Ireland as the region reached an unwanted milestone for non-governance.
On Tuesday the region notched up 589 days since the powersharing executive collapsed – passing Belgium for the world’s longest peacetime period without a properly functioning government.
While Northern Ireland will avoid an embarrassing entry in the Guinness Book of World Records – the Stormont impasse was ruled ineligible as it only relates to a devolved administration – the day will be marked by a series of public protests.
The #wedeservebetter events will be held in a series of cities and towns across the region on Tuesday evening.
The executive imploded in January 2017 amid a bitter row between the Democratic Unionists and Sinn Fein over a botched renewable energy scheme.
The rift widened to take in other more tradition disputes – such as the Irish language – and the parties remain at loggerheads, with no prospect of an imminent breakthrough on the horizon.
While there has been speculation over a new round of negotiations for the autumn, no date has publicly been announced.
Ahead of the demonstrations, a spokeswoman for Secretary of State Karen Bradley said: “The Secretary of State is acutely aware of the deep frustration and difficulties faced by the people of Northern Ireland and the urgent need to resolve the current impasse.
“She shares the firm view that the current situation cannot be allowed to continue and is working on options to ensure the good governance of Northern Ireland.
“The UK Government’s priority is to secure a basis for political talks and re-establish a locally elected, democratically accountable devolved government at the earliest opportunity.
“In the absence of an Executive, the Secretary of State continues to take the necessary decisions to protect the interests of Northern Ireland and ensure stable public finances, demonstrated by the recent Budget Act.”
The crisis was triggered on January 9 2017 when the late Sinn Fein deputy first minister Martin McGuinness quit. The executive collapsed one week later – on January 16 – when the deadline for Sinn Fein to nominate a new minister expired. Tuesday marked 589 days since the latter date.
Belgium was without a properly functioning government for 589 days when Prime Minister Yves Leterme quit in April 2010, and it went 541 days without any government at all when a new administration was not formed after a subsequent election in June 2010
Guinness uses the 541-day timeframe for measuring the world record.
In Northern Ireland, the administration limped on without a first or deputy first minister until March 2 2017 – when a snap Assembly election was held.
Using the measure of the time without no government at all, Northern Ireland passed 541 days last Friday, on August 24.
- Press Association
Update 10.18am: Northern Ireland is set to break the world record for the longest peacetime period without a government at Stormont.
The North has been without a government for more than 500 days after the Assembly collapsed in January 2017.
Belgium holds the current record of 541 days without an elected government from 2010.
The Irish and British governments have said there will be a new round of talks in autumn in an attempt to restore power-sharing.
"It's extremely embarrassing," said Colum Eastwood, leader of the Social Democratic and Labour Party.
"We have crises in our hospitals, crises in our education system, jobs not getting delivered, government contracts not being put out there.
"No decisions are being taken."