BAGHDAD- Iraq on Thursday carried out air strikes on Islamic State positions in Syria a week after Prime Minister Haider al-Abadi said his country would defend itself from militant threats across the border.

Iraqi F-16 warplanes crossed into Syria to carry out the strikes after coordination with Syrian President Bashar al-Assad's government, an Iraqi military spokesman said.

"Carrying out air strikes on Daesh gangs in Syrian territories is because of the dangers posed by said gangs to Iraqi territories and is proof of the improved capabilities of our armed forces," the Iraqi military said in a statement.

Earlier this month, Abadi had said Iraq would "take all necessary measures if they threaten the security of Iraq", referring to the jihadist militants who just three years ago overran a third of Iraq.

The prime minister declared final victory over the ultra hardline group in December but it still poses a threat from pockets along the border with Syria and has continued to carry out ambushes, assassinations and bombings across Iraq.

Iraq currently has good relations with Iran and Russia, Assad's main backers in the seven-year Syrian civil war, while also enjoying strong support from the U.S.-led coalition.

(Reporting by Ahmed Aboulenein; additional reporting by Maher Chmaytelli; editing by Raya Jalabi/Mark Heinrich) ((maher.chmaytelli@thomsonreuters.com; +9647901917030;))