Is Iraq now a regional war?

So apparently the US is sticking by its story on the Iranian military officials arrested in Iraq last week.

The NY Times reported on this Monday; and today in another article, a US military spokesman insisted there was evidence linking them to attacks on coalition forces.

Does this mean that a larger regional war has already started? Or is this an attempt to minimize the possible benefits of direct negotiations with Iran on Iraq? Or perhaps this is part of a larger crackdown on the militas:

The predawn raid on Mr. Hakim’s compound, on the east side of the Tigris, was perhaps the most startling part of the American operation. The arrests were made inside the house of Hadi al-Ameri, the chairman of the Iraqi Parliament’s security committee and leader of the Badr Organization, the armed wing of Mr. Hakim’s political party.