A key Syrian opposition group on Sunday accused the government in Baghdad of intervening in the country and "attacking the Syrian people," a day after clashes were reported near the border.
"After the Iraqi government headed by (premier) Nuri al-Maliki gave political and intelligence support to the Syrian regime... the Baghdad regime has moved on to a new level of intervention in Syrian affairs," the Syrian National Council said.
It charged that Baghdad was "attacking the Syrian people, their basic rights and their territorial sovereignty."
An Iraqi official said on Sunday that one Iraqi soldier was killed and three people including a soldier were wounded inside northern Iraq during a gunfight near a border post the day before.
The casualties were caused by "fighting at the Yaarubiyeh border crossing inside Syria" between regime forces and rebels on Saturday, defence ministry spokesman Mohammed al-Askari told AFP.
Four Syrian soldiers were also treated at an Iraqi hospital after the clash, Askari added.
The SNC called on the Arab League and the United Nations to condemn Baghdad for what it called an attack "on Syrian sovereignty," saying the international community should "at the very least condemn this aggressive behaviour."
Baghdad has pointedly avoided calling for the departure of Syrian President Bashar al-Assad, who is locked in a bloody civil war with rebels opposed to his regime, and has instead urged an end to violence by all parties.
But US officials have repeatedly called on the Iraqi government to halt Iranian flights to Syria via Iraqi airspace, which they say are transporting weapons to Assad's forces.
As the violence has escalated in Syria, the country's crisis has spilled over into neighbouring countries Lebanon and Iraq.