The Third Armoured Cavalry Regiment (3rd ACR) raided what it called "suspected foreign fighter" camps along the Syrian border and captured four people, one of whom was on a wanted list.
The military said it had arrested a total of 20 people around the western al-Anbar province, home to the flashpoint towns of Ramadi and Falluja.
The 4th Infantry Division arrested 22 people in the area north of the capital, including Saddam's hometown of Tikrit.
US troops have been increasingly facing resistance in and around Baghdad, from what they claim is a combination of Saddam supporters and foreign fighters.
Review of contracts
The Pentagon is showing a change
of heart over contracts
The arrests come as the US signalled on the diplomatic front that it is willing to review its policy barring companies from countries that opposed the war on Iraq from bidding for rebuilding contracts.
Bidding is likely to open this week for the US-funded contracts.
A Pentagon ruling last month excluded firms from nations that did not support the war, a decision that riled traditional allies such as France and Germany, which opposed America's decision to invade Iraq.
The Pentagon told prospective bidders via a government procurement website on Monday (www.fedbizopps.gov) that a list of eligible countries for projects funded by $18.6 billion in US funds was being reviewed.
"This list is under further consideration, however, and may be revised," said the document issued by the Office of the Secretary of Defence, which said the original list of 63 countries remained valid.
Diplomatic sources in Washington said they had noticed signs of a softening by the US government over who could apply for prime contracts, following a mission by ex-US secretary of state James Baker to Europe last month to seek forgiveness of Iraq's crippling debt.