James Jeffrey, a former U.S. ambassador to Iraq, said Sunday on CBS's "Face the Nation" that withdrawing troops from Iraq has led to a weaker Iraqi army and made U.S. counterterrorism operations more difficult.

When asked whether pulling out troops has led to the current situation in Iraq, Jeffrey said it had "a certain effect."

"We would have had a better-equipped Iraqi army," he said. "We would have had better eyes on what the problem was.  And would have been able to do certain counterterrorism operations."

But the psychological effect, he said, was the most important.

"We would have still had a stake in that country, and we would have cared more for what Maliki was doing," he said, referring to Iraqi Prime Minister Nouri al-Maliki. "And we would have more leverage to change it."

Jeffrey said Maliki will not be able to put together an inclusive government, which he has failed to do in the past eight years despite U.S. pressure.

"The pressure is on him to basically step down," he said. "The parliament has to elect a new government after the elections. And it does not look good for Maliki, but he's resisting. The Shia coalition, which has a majority in parliament, or close to it, have to decide on an alternative.  This is going underway day and night right now."