Abdul Mahdi said Iraq sought to move beyond its current arrangement with Syria - under which it launches air strikes against Islamic State militants in Syrian territory.
Iraq's prime minister said on Sunday that top security officials from Baghdad had met Syrian President Bashar al-Assad in Damascus, and hinted at a bigger Iraqi role fighting Islamic State militants as US troops withdraw from Syria.
"This issue has a lot of complications," Adel Abdul Mahdi told reporters, referring to US President Donald Trump's surprise announcement this month that he will withdraw US forces from Iraq's neighbour.
"If any negative development takes place in Syria it will affect us. We have a 600 km (400 mile) border with Syria and Daesh (Islamic State) is there," Abdul Mahdi said.
The premier said the Iraqi delegation had visited Damascus to "gain the initiative, not just deal with the consequences" of any future Islamic State (IS) activity emboldened by the US withdrawal. Iraqi news websites said the visit took place on Saturday.
Abdul Mahdi said Iraq sought to move beyond its current arrangement with Syria - under which it launches air strikes against Islamic State militants in Syrian territory - but did not got into more details.
"There are groups operating in Syria, and Iraq is the best way to deal with this," he said, responding to a question about the possibility of increased involvement of Iraqi forces in Syria.
Iraqi Shi'ite Muslim paramilitary groups backed by Iran already operate inside Syrian territory against the Sunni Muslim militants of Islamic State.
Abdul Mahdi has previously said that about 2,000 Islamic State fighters are operating near the border in Syria and trying to cross into Iraq.
Islamic State was militarily defeated in Iraq in 2017, but has continued to launch guerilla-style attacks on security forces in the north of the country.