"Recently it has been seen that American army helicopters were flying a small distance from Iraq's border with Iran and, because of the closeness to the border, the danger of them violating Iran's border is possible," the statement by the General Staff of Iran's Armed Forces said.
"Iran's armed forces will respond to any violation," it said.
Iran will "take down" any overflying aircraft which fails to respond to warnings, a high-ranking Iranian air force commander told FNA.
The statement also urged US commanders in Iraq to keep their forces a secure distance from the borders to avoid any risks.
The air force commander said his country's reaction to any incursion would go beyond warnings.
"If something happens, we will carry out all the steps from giving a warning to taking down the detected (foreign) airplanes according to regulations," the commander told FNA.
"Due to the threats posed by enemies in recent months, the armed forces are at the highest level of preparation and all of our warnings will be definitely doable," he said.
The commander also said that in the past month the country's forces have dealt with two foreign aircraft that entered Iran's air space without permission.
On October 7, Iran forced down in its territory a Hungarian aid plane, carrying soldiers from the US and some other NATO member states.
US forces launched a helicopter raid on a Syrian border village with Iraq on October 26 in which eight civilians including children were killed.
A US official in Washington claimed that the operation targeted a top militant who smuggled arms and fighters into Iraq.
Iran's Foreign Minister Manouchehr Mottaki on Monday during a visit to the Syrian capital denounced the raid and expressed "the solidarity of the Iranian people with the Syrian people after the American raid".
The statement from Iran's army headquarters comes after Americans elected their next president, Barack Obama, who has said he would toughen sanctions on Iran but has also held out the possibility of direct talks with Tehran.
Washington, which has not had diplomatic ties with Tehran since 1980, accuses Iran of seeking to build nuclear weapons, without having any corroborative evidence to substantiate its allegations against the Islamic Republic.
Tehran vehemently denies the charges, saying that it wants atomic technology to make electricity and save its oil and gas for export.
Obama, like Bush, has not ruled out military action although he has criticized the outgoing administration for not pushing for more diplomacy and engagement with Iran.
"Change of political figures is not important by itself. What is more important is a change of American policy," Ali Agha-mohammadi, a close aide to Iran's Supreme Leader Ayatollah Seyed Ali Khamenei, said.
Iran has warned it would respond to any attack on its territory by targeting US interests and America's ally Israel, as well as closing the Strait of Hormuz, the waterway at the mouth of the Persian Gulf and vital route for world oil supplies.
But some analysts were cautious, saying Obama had to show he was offering more than a change in style from Bush.
"It is for the Americans to show that something has changed, not the Iranians," Tehran University professor Mohammad Marandi said.
In a Sep. 11 report, the Washington Institute for the Near East Policy says that in the two decades since the Iran-Iraq War, the Islamic Republic has excelled in naval capabilities and is able to wage unique asymmetric warfare against larger naval forces.
According to the report, the Islamic Revolutionary Guards Corps Navy (IRGCN) has been transformed into a highly motivated, well-equipped, and well-financed force and is effectively in control of the world's oil lifeline, the Strait of Hormuz.
The study says that if Washington takes military action against the Islamic Republic, the scale of Iran's response would likely be proportional to the scale of the damage inflicted on Iranian assets.
Intensified threats by Tel Aviv and Washington of military action against Iran contradict a recent report by 16 US intelligence bodies which endorsed the civilian nature of Iran's nuclear plans and activities.
Following the US National Intelligence Estimate (NIE) and similar reports by the IAEA head - one in November and the other one in February - which praised Iran's truthfulness about key aspects of its past nuclear activities and announced settlement of outstanding issues with Tehran, any effort to impose further sanctions or launch military attack on Iran seems to be completely irrational.
The February report by the UN nuclear watchdog, the International Atomic Energy Agency, praised Iran's cooperation in clearing up all of the past questions over its nuclear program, vindicating Iran's nuclear program and leaving no justification for any new UN sanctions.
The UN nuclear watchdog has also carried out at least 14 surprise inspections of Iran's nuclear sites so far, but found nothing to support West's allegations.
Following the said reports by the US and international bodies, many world states have called the UN Security Council pressure against Tehran unjustified, demanding that Iran's case be normalized and returned from the UNSC to the IAEA.
Meantime, a recent study by the Institute for Science and International Security (ISIS), a prestigious American think tank, has found that a military strike on Iran's nuclear facilities "is unlikely" to delay the country's program.