Just under 13,500 Ukrainian refugees have arrived in Ireland, according to the Minister for Justice Helen McEntee.
Arriving at an emergency meeting of EU justice and interior ministers in Brussels, Ms McEntee said 93% had arrived via Dublin Airport.
However, more and more Ukrainians were now travelling across Europe by bus and train, than getting flights from other countries.
Some 3.9 million have fled Ukraine in total, with 2.2 million of those entering Poland.
The EU is giving refugees "temporary protection" status, meaning they can live, settle and work in the EU for a period of time.
EU ministers are expected to devise an anti-trafficking plan given that 90% of those fleeing are women and children.
"What's really important… is that we acknowledge the risks with such a mass movement of people. Risks around human trafficking, child exploitation, but also criminality," Ms McEntee said.
"What we need to make sure is that as people start to disperse further from the initial member states, that we are collectively speaking to each other that we know where people are travelling to, and that obviously we can see where people are seeking that temporary protection mechanism," she said.
The minister said it was hard to predict how many refugees would come to Ireland overall.
"We're not going to put a cap on this," she told RTÉ News. "But I think the more coordinated we are, the more we will be able to respond effectively, whether it's providing accommodation, whether it's preparing schools for children, whether it's making sure we have access to health care for people."
Ministers will discuss financial support for front line states. Minister McEntee said that was where the primary focus was, but if funding became available for Ireland the Government would look at it.
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Minimum sentencing for murder convictions
Separately, Ms McEntee confirmed that Department of Justice officials were exploring the idea of giving judges discretion to put a minimum sentencing level where certain kinds of murder convictions were concerned.
"I have been considering the issue of sentencing and in particular mandatory sentences for some time," she said.
"I've asked my team to look at potentially giving discretion to judges, where life sentences are handed down, be it in murder cases or other types of cases, because there are some real life sentence are handed down, where a judge would have a discretion to say that a person cannot come before the parole board before X amount of years," she said.
Currently those convicted of murder come before the parole board for assessment after 12 years.
"What we are exploring is the possibility that in really heinous types of crimes, really awful crimes, that a judge would have the discretion to say, this person cannot come before the parole board for at least 20, 25, 30 years.
"So, it leaves the discretion with the judiciary. It doesn't in any way step over the really important work of the parole board. But it acknowledges that there are some types of crimes [where] really there should be tougher sentences."
Rise in Covid-19 infections
On the upsurge in Covid cases, the minister said that despite the surge the numbers of people entering hospital only because of Covid were going down.
She said: "Half of the people in hospital have not actually gone in because of Covid. And while our numbers in ICU are slightly increasing, people actually going in because of Covid is decreasing. So, while the numbers are quite high, all the signs would point to the fact that our vaccination program is still working, and that we need people to be vigilant."
She added: "I don't want to be in a situation where we're looking to reinforce restrictions. So what we're asking people is to remain vigilant, keep washing your hands, keep making sure that you abide by advice and wear masks where you're in crowded areas.
"The Chief Medical Officer is constantly talking to the Minister for Health…and if any changes are to be required we'll certainly take them on board."
