Observers have pointed out that logistical support usually comes from the military, which is largely tied up Tigray, leaving organisers short on manpower.
Prime Minister Abiy Ahmed and his Prosperity Party face challenges from increasingly strident ethnically-based parties seeking more power for their regions.
"We will let everybody (know) soon as to how many additional weeks/days to complete the delayed tasks ... Wouldn't be more than 3 weeks," she added.
"There is a broad acknowledgement that these elections won't be perfect, to say the least -- that there will be shortcomings, there will be grounds for criticism and for a lot of improvement," a Western diplomat said.
"They are receiving support from the South Sudanese Ministry of Refugee Affairs," Dujarric continued, and the UN High Commissioner for Refugees (UNHCR) is "aware" of the situation and in contact with South Sudanese authorities.
Grandi, the UNHCR head, visited Ethiopia, including the Mai Aini refugee camp, over the weekend for the first time since the conflict began in November. The camp is one of two camps in southern Tigray the UN has been able to access.
But the impromptu parade this month in Alamata, a farming town in southern Tigray flanked by low, rolling mountains, was unrelated to any kind of battlefield victory.
The ultimatum was rejected by the leaders of the region, whose forces have been fighting federal troops in the country's north for three weeks, displacing over 40,000 people and killing hundreds.
The government said Tuesday that "a large number of Tigray militia and special forces are surrendering" following the issuance of Abiy's 72-hour ultimatum.