(Adds State Department comment, background, paragraphs 7, 10-12)
By Mark Hosenball and Missy Ryan
WASHINGTON, Aug 11 (Reuters) - The U.S. government is directly supplying weapons to Peshmerga fighters from Iraq's semiautonomous Kurdish region to help them fight Sunni militants, in a deepening of America's military involvement in Iraq, U.S. officials said on Monday.
The Kurdish fighters are struggling to stem advances by militants from the Islamic State, an al Qaeda offshoot.
The officials said the weapons were supplied by the Central Intelligence Agency but that the Pentagon may soon start arming the Kurdish fighters, who regained control of two strategic towns in northern Iraq on Sunday with help from U.S. airstrikes.
The officials declined to specify when the supply program began or what sort of arms it included.
Weapons have also been shipped in three deliveries from the Iraqi government in Baghdad to Arbil, capital of Iraqi Kurdistan, consisting mostly of AK-47 assault rifles and ammunition, the U.S. officials said.
Reuters reported on Friday that the Iraqi government had sent a first, unprecedented shipment of ammunition to Arbil.
U.S. officials have said they were previously reluctant to give arms directly to the Kurds because of a desire to see Iraq remain a unified state and a hesitancy to do anything that might bolster Kurdish ambitions for autonomy.
U.S. President Barack Obama has faced criticism for being reluctant or too slow to intervene in thorny foreign policy issues which have piled up under his watch, including the dramatic rise of the Islamic State, which has seized control of large swathes of land in the north and west of OPEC member Iraq.
A senior U.S. defense official acknowledged that the United States was providing arms and ammunition needed by the Kurds but said it was not coming from the Department of Defense. Officials said the Pentagon was in discussions about how to increase its military support to the Kurds and could soon approve a decision to directly supply weapons.
FIRST SINCE 2011
The U.S. State Department said the U.S. government was "working" to provide arms directly to the Kurds, saying they needed them badly and that the United States was doing what it could to accelerate deliveries.
"The government of Iraq has made deliveries from its own stocks to the Kurds and we are working to do the same in coordination with all the relevant parties," State Department spokeswoman Marie Harf told reporters.
"The Kurds need additional arms. We are providing those."
Last week, Washington launched its first military action in Iraq since pulling its troops out in 2011. U.S. warplanes bombed Sunni insurgents from the Islamic State, who have marched through northern and western Iraq since June.
Washington says it is taking limited action to protect the Kurdish autonomous region and prevent what Obama called a potential "genocide" of religious minorities targeted by the militants.
The militants made new gains against Kurdish forces despite three days of U.S. airstrikes, while Baghdad, long braced for the Sunni fighters to attack, was now tensing for possible clashes between forces loyal to Prime Minister Nuri al-Maliki and those of his rivals after Iraq's president named a new prime minister on Monday.
Obama says a more inclusive government in Baghdad is a precondition for more aggressive U.S. military support against the Islamic State. He has rejected calls in some quarters for a return of U.S. ground troops, apart from several hundred military advisers sent in June.
The Islamic State, which sees Shi'ites as heretics who deserve to be killed, has ruthlessly moved through one town after another, using tanks and heavy weapons it seized from soldiers who have fled in their thousands.
On Monday, police said the militants had seized the town of Jalawla, 115 km (70 miles) northeast of Baghdad, after driving out the Kurds' Peshmerga forces.
Washington and its European allies are considering requests for more direct military aid from the Kurds, who have themselves differed with Maliki over the division of oil resources and who took advantage of the Islamists' advance to expand their territory. (Additional reporting by David Alexander and Arshad Mohammed.; Editing by Jason Szep and Howard Goller)