More than 300 male evacuees have been held for screening after leaving the Old City under an agreed ceasefire.
Talal Barazi, governor of Homs, says 111 men have been questioned and released, while 190 others are still being held.
More than 1,100 people have fled the city since Friday under a truce.
Aid organisations in Syria had hoped to evacuate more civilians on Tuesday after the ceasefire was extended by three days, but the operation was delayed by a day due to logistical reasons.
"The evacuation of civilians and delivery of food aid will continue tomorrow morning,"  the regional governor told the AFP news agency.
A truce agreed until Wednesday night could be extended if necessary, he added.
The UN human rights office says it is "deeply concerned" that boys and men were seized as they left the besieged area.
"It is essential that they do not come to any harm," said Rupert Colville, spokesman for the UN commissioner for Human Rights.
"We will continue to press for their proper treatment according to the international humanitarian and human rights law."
Melissa Fleming, spokeswoman for the UN High Commissioner for Refugees (UNHCR), said detainees were being held at an abandoned school.
"We are monitoring the situation. We are definitely taking account of the number there and who is there," she said.
Meanwhile, face-to-face negotiations between Syrian government and opposition delegations in Geneva have been adjourned for the day.
A second round of peace talks was held on Monday with separate meetings between UN envoy Lakhdar Brahimi and the two sides.
"The beginning of this week is as laborious as it was in the first week. We are not making much progress," he told a news conference at the United Nations headquarters.
The first round ended last month with no firm agreements and both sides trading insults.
The opposition wants the government to commit in writing to the 2012 Geneva Communique, which called for the formation of a transitional administration with full executive authority.
President Bashar al-Assad's government has ruled out any transfer of power.
On the ground, efforts to evacuate hundreds more women, children and elderly people from Homs, which has been under siege for 18 months, were temporarily halted on Tuesday for logistical reasons.
More than 450 civilians left on Monday, amid mortar fire and shooting.
The BBC's Lyse Doucet, who is in Homs, said it was not expected that so many young men would try to leave.
So their fate is being scrutinised very closely, our correspondent adds.
She was at a press conference on Tuesday where the Homs governor gave the latest figures on how many detainees had been released.
He said he expected around 80% of those held would be let free.
Matthew Hollingworth, Syria director for the UN's World Food Programme, told the BBC "the floodgates have opened" as many more people try to leave.
"The levels of destitution inside the Old City are like nothing I've ever seen before," he said.
"People are living in tunnels underground, moving between shells of buildings to find roots to eat - there has been little food for many, many months now."
UN aid chief Valerie Amos welcomed the extension of a three-day truce on Monday.
Desperation of Palestinian refugees
But she also confirmed that 11 people were killed after the relief operation was "deliberately targeted". It is unclear who was responsible for the attack.
She said that many of those who had left the city so far appeared traumatised and weak after enduring many months of siege.
Writing in the UK's Independent newspaper, UK Foreign Secretary William Hague warned that the Srebrenica massacre of 1995 - when more than 8,000 men and boys were killed in a Bosnian town - could be repeated in the Old City of Homs.
He said it was time to "turn up the heat" on the Syrian government.
However, Russia and China failed to attend a meeting in New York to discuss a new UN Security Council resolution calling for greater access for humanitarian aid on Monday.
Russian Foreign Minister Sergei Lavrov has dismissed the draft resolution as one-sided and "detached from reality", according to Interfax news agency.
Syria's civil conflict has claimed more than 100,000 lives since 2011 and has driven 9.5 million people from their homes.
UN aid agencies have expressed concern about the safety of scores of men and boys detained by the Syrian authorities after being evacuated from Homs.