Iraq's parliament went home Tuesday without resolving calls from within that nation for the resignation of Prime Minister Nouri al-Maliki. Now the country is settling down for the coming battle of Baghdad between the jihadist Sunni group ISIS and the Shia militias, many of which look to Iran for support. Mr. Maliki, turning his back on President Barack Obama's offer of help, is looking instead to Iran and Russia.

Nevertheless, President Obama is boosting his commitment of U.S. troops to Iraq, adding 300 combat soldiers to the 300 Special Forces personnel he recently sent as advisers to the Iraqi army. According to The Washington Post, there are now 775 U.S. troops in Iraq.

Let us hope that these forces have been given the mission of safely extracting Americans from Iraq, after which they will come home. It is clear that a U.S. military presence is no longer wanted by the Shia-dominated Iraqi government. With every passing day, Americans in Iraq face rising danger.

It's been just over a week since Secretary of State John Kerry went to Iraq promising "intense and sustained" assistance, though apparently not the air combat support requested by Prime Minister Maliki, who was urged by Mr. Kerry to step down in the interests of a government giving equal weight to Kurd, Sunni and Shia interests.

Mr. Kerry got his answer almost immediately. Last Wednesday, Mr. Maliki rejected calls for a national reconciliation government as "a coup against the constitution." On the next day he welcomed a Syrian air strike on ISIS, denounced the United States for delaying the delivery of aircraft, and announced his purchase of warplanes from Russia.

Meanwhile, Iran's supreme leader, Ayatollah Ali Khamenei, made it clear that he is "strongly opposed" to any American involvement in Iraq, characterizing the civil war as a dispute "between those who want Iraq to join the U.S. camp and those who seek an independent Iraq."

Of course ISIS is not any part of "the U.S. camp," but the message to Mr. Maliki was clear: Reject the Americans if you want our help. ISIS, by exploiting Sunni anger at the Shia-dominated Iraqi government, threatens to split Iraq into three ethnically and religiously distinct areas, with the Kurds in the north, a Sunni belt up to the outskirts of Baghdad (including Baghdad if ISIS can take it) and reaching across Syria to the Jordanian border. What's left of Iraq would presumably remain under Shia control.

On the other hand, Iran is fighting in Iraq and Syria to create a Shia-controlled stretch of territory running from Iran to the border of Israel.

Both the ISIS plan and the Iranian plan pose major threats to America's key ally, Israel.

The preferred course of action may be to let the two opponents exhaust themselves by fighting it out and then deal with the consequences. But there are likely to be troublesome side-effects, beginning with an ISIS threat to Jordan, that will have to be dealt with as they occur.

All of this might have been avoided with a more pro-active Obama policy for helping the non-jihadist Syrian opposition.

And obviously, President George W. Bush's decision to invade Iraq in 2003, and the subsequent mistakes he and his team made before the success of their 2007 U.S. troop "surge" strategy, are fair targets for criticism.

But President Obama didn't capitalize on the surge's positive outcome. After more than 5 years in the White House, he also bears some responsibility for what has - and will - happen in Iraq.

At this sad point, though, U.S. blunders there are water over the dam.

Now the whole Middle East is riding the rapids of rising chaos in Iraq.