WELLINGTON -- New Zealand is to open an embassy in Iraqi capital as its troops begin a two-year mission to train Iraqi forces in the fight against Islamic State insurgents.

The embassy would be "co-located" with the Australian Embassy in Baghdad and headed by a career diplomat, who would take up his post next week, Foreign Minister Murray McCully said Thursday.

"Our resident ambassador will be charged with supporting New Zealand's non-combat training mission to Iraq and assessing how we can better support and build relations with the Iraqi government," McCully said in a statement.

"Our embassy will also be responsible for maintaining relations with the United Nations Assistance Mission for Iraq."

Up to 143 New Zealand troops are in Iraq, where they operate a joint training mission with Australian forces at Camp Taji, just north of Baghdad.

Prime Minister John Key rejected calls on Tuesday to pull the troops out after Islamic State forces overran Ramadi, about 100 km away from Baghdad, and US Defense Secretary Ash Carter criticized Iraqi Security Force troops for lacking the "will to fight."