Around 399 people fleeing the wartorn country have been matched by sponsors in Leeds who are ready to welcome them into their homes.
But of those, only 46 have arrived in the city thus far, although many more have been granted visas to come.
The Home Office has received widespread criticism for the speed at which visa applications for Ukrainian refugees are being processed.
But Leeds’ Conservative group leader said the government was having to work “on the hoof”, as it dealt with the crisis.
Paul Money, chief officer of Leeds City Council’s safer communities unit, said the situation was “fluid”.
He told a meeting of senior councillors on Tuesday that more than a third of those due to arrive in Leeds are children, while the oldest refugee is aged 77.
Mr Money said: “Of the 399, they are made up of 250 females, 82 males and 67 individuals whose gender is unspecified for a number of reasons.
“We’re working through a process of safeguarding and DBS checks of sponsors.
“Where children are due to join sponsors, we are doing enhanced DBS checks.
“In terms of the visas, checks this morning with the Home Office have advised that they’ve issued a total of 154 visas (to Leeds-bound refugees), with a number obviously still pending.
“Obviously not all of those 154 have arrived in the city.”
The council has carried out checks on homes where people have offered to accommodate refugees.
While most have been judged adequate, Mr Money said that five properties had been deemed unsuitable.
Meanwhile, the Reginald Centre on Chapeltown Road will be used as a base to help deliver services to refugees when they arrive, partly because it is a minute’s walk from the city’s Ukrainian Community Centre.
The leader of Leeds’ Conservative group, Councillor Andrew Carter, said it was important that support for traumatised war victims was in place for when they arrive.
He also suggested there was a security risk posed by pockets of the eastern Ukrainian population who he said had previously “identified very strongly with the Russian state”.
He told the meeting: “It’s not easy therefore to simply start opening the doors and letting everyone you would like to come in without the proper checks and balances.
“The Home Office to be fair are under huge pressure to speed up the visa scheme for reasons we should all understand.
“But we should also understand what speeding up the system means. We need to be careful we’re putting in place the proper support packages for these poor people.
“We’ve talked about the effects of Covid. How about the effect of watching members of your family shot, your home blown up and your country devastated?”
“We can only do what we can do in this period of time where they are our guests and we must look after them.”
But Liberal Democrat group leader Stewart Golton said: “One thing you don’t do with welcome guests is make them wait at the door.
“I’m not sure how much a security threat mothers and chidlren are to this state and therefore they shouldn’t be subject to such security checks, which actually delays them getting to these shores.”