Iraqi Kurdish leader Massoud Barzani had said earlier this month that his well-armed region was ready to defend Kurds living in north-eastern Syria if they were being threatened by rebels.
But despite safety concerns which have driven thousands to flee, his chief of staff said that did not mean that Iraqi Kurdistan was considering sending troops across the border.
Mr Hussein said any such measure would drag the region deeper into a conflict that has increasingly split it down ethnic and sectarian lines.
"Our policy is not to intervene militarily," Mr Hussein told reporters in the regional capital Arbil.
"I think the Kurds in Syria have got their own people to defend them.
"They do not need military units to go there, but perhaps they need other kinds of support," he said.
He said that Iraqi Kurdistan could help co-ordinate international aid and predicted that more people would flee after about 40,000 mainly Kurdish Syrians crossed the border in the past two weeks.
Regional officials refer to north-eastern Syria, where most Syrian Kurds live, as "Western Kurdistan."
There are many Kurds in Syria, Turkey and Iran but have no state of their own. They have an autonomous regional government in Iraq.
UN refugee officials have predicted that up to 100,000 Syrians could flee to Iraq within the next month.
Mr Hussein urged Syrians not to leave unless absolutely necessary, saying he feared the exodus may turn attention away from Kurdish political issues.
"We are worried about having an empty Kurdistan in Syria because if the population leaves we will also lose that part of Kurdistan," he said.
The influx of refugees last week was so large and sudden that border officials shut a pontoon bridge connecting the two countries, fearing it would collapse under the weight of people.
Refugee camps grew so fast in the past week that there is still a waiting list for tents and food and medical supplies are scarce.