COPENHAGEN- The United States hopes to discuss the entire strategic framework of its relationship with Iraq soon, a U.S. envoy said on Tuesday, as the fate of a U.S. military mission there remains in doubt after a drone strike that killed an Iranian general.

Iraq's parliament has voted to ask the United States to withdraw its 5,000-strong force after the Jan. 3 U.S. drone strike in Baghdad, which killed Iranian general Qassem Soleimani and the Iraqi leader of a powerful pro-Iran armed faction.

Washington has paused some of the military activity of its troops in Iraq, which were invited back into the country in 2014 as part of a mission to fight the Islamic State militant group in both Iraq and Syria, after withdrawing three years earlier.

"We are looking forward to sitting down and having a broad discussion with the Iraqi government of our entire strategic framework relationship in the near future," James Jeffrey, the U.S. special envoy for Syria, told Reuters.

Jeffrey said U.S.-led coalition operations were still on pause in Iraq as the focus has been on force protection and talks with the Baghdad government on the way forward.

Iraq is an ally of both the United States and Iran, and has had to balance those relationships carefully at a time of escalation between the two foes. Recent months have seen demonstrations in Iraq against both countries' influence.

President Donald Trump responded angrily to demands from Baghdad that U.S. troops withdraw from Iraq, even threatening to impose sanctions if the troops were forced out. He met Iraq's president, Barham Salih, on the sidelines of the World Economic Forum in Switzerland last week.

Jeffrey said the United States supports a possible future role by NATO in Iraq and Syria.

"Nobody is rushing anything," Jeffrey said when asked about the time frame for talks with the Iraqi government. "We are very interested in NATO's process of seeing what additional role it can do."

The past week had seen no spike in activities of Islamic State in neither Iraq or Syria, but activity levels remained at a level that caused concern, Jeffrey said.

(Reporting by Jacob Gronholt-Pedersen; Editing by Peter Graff) ((copenhagen.newsroom@thomsonreuters.com; +45 3396 9673; Reuters Messaging: jacob.pedersen.thomsonreuters.com@reuters.net))