Of those, 486 arrived into the country on Sunday.
Martin said roughly two thirds of the arrivals have family members residing in Ireland, but that figure is expected to decrease as more arrive.
Cabinet will meet on Tuesday morning to discuss plans regarding the intake of refugees, with as many as 80,000 predicted to arrive in Ireland.
"This is a major humanitarian crisis on the continent of Europe, and the response to that will have to be outside of the norm," Martin said. "It can't be business as usual in terms of how one responds to that and Government will be giving this consideration tomorrow morning at its Cabinet meeting."
Cabinet is expected to explore the use of modular homes on state land, while members of the public may be asked to take refugees into their homes on a voluntary basis.
A portal is due to be established this week to coordinate offers of help from the public.
Minister for Health Stephen Donnelly said that those arriving from Ukraine will receive medical cards and have full access to healthcare.
Martin said he believes the United Nations' "relationship with Russia will never be the same again, given the nature of this attack on so many people."
