The Department of Homeland Security responded in a statement released to the U.S. News and World Report.
DHS told Whispers it regularly fills all of its goods and services requirements at one time because it's cheaper for the agency, and that the 1.6 billion number was misleading because the language of DHS's purchase said it would need "up to" a certain amount.
"DHS routinely establishes strategic sourcing contracts that combine the requirements of all its components for commonly purchased goods and services such as ammunition," a DHS legislative affairs person wrote to Coburn. "These strategic sourcing contracts help leverage the purchasing power of DHS to efficiently procure equipment and supplies at significantly lower costs," the department told Coburn.
A detailed breakdown of the purchases can be found here. The report breaks down utility and purchases by department, which appear to be in line with previous years. The number of rounds purchased was 150mil in 2010, and around 100mil in 2011 and 2012. If anything, the number of purchased rounds is going down. The requested budget allows for 320 million rounds 2013, but that does not mean that the DHS will actually purchase the rounds. The agency has spent $36mil on ammo in 2012, and approximates spending $37mil in 2013, an estimated increase of 2.7% (not adjusted for inflation).
I refer you to this article in the Military Times that discusses these numbers in greater detail.
Note also that according to the National Shooting Sports Foundation, 10-12 billion rounds are produced domestically per year, with "many more billions" of foreign imports. Which would mean that the government is approved (and not guaranteed) to buy up to 2.6% of the national production per year, and a smaller number if we account for foreign imports. Mr. Nayak and Bert Medina, director of the Immigration and Customs Enforcement National Firearms and Tactical Training Unit put that number closer to 1%. Given that these estimates don't account for the existing inventory or unused manufacturing capacity, it seems the effects of the purchase are at best modest.
Finally, note that the conspiracy theories about the government stockpiling ammo surface yearly around the budget time, and are propagated by conspiracy blogs that don't bother to read the released documentation. See for example the note on Skeptic Blog by Brian Donning from 2012.
To conclude: (1) The documentary evidence speaks to the government's explicit intent of "procuring supplies" for the arms-bearing departments under the umbrella of the department of homeland security. These procurements are coordinated among multiple agencies, and at levels consistent with their purchases in the past few years. There is no mandate or evidence of collusion between these agencies to limit the market.
(2) By conservative estimates, the government is approved to purchase between 1% and 2.6% of only the domestic supply of ammunition per year, constraining the potential impact on the market to these numbers.