By Suadad al-Salhy

BAGHDAD (Reuters) - Iraq's Prime Minister Nuri al-Maliki encouraged Syria to open up its political system to end one-party Baath rule as part of reforms in the face of months of popular protests.

Maliki's comments about his neighbor came as Syrian President Bashar al-Assad faces increasing international condemnation and sanctions over a crackdown on protests that the United Nations says has killed more than 2,900 people.

Iraq's Shi'ite-led government says it seeks balance in its relations in the Arab region, but its approach to Syria has been caught between supporting Damascus, an ally of Shi'ite power Iran, and concern over unrest spilling over into Iraq.

Maliki, who lived in Syria until he returned to Iraq after the 2003 invasion toppled Saddam Hussein, has taken a more muted approach to the Syrian crisis than Sunni Arab leaders.

"Certainly, we support the idea of ending one-party rule, rule by one person," he told Reuters when asked about what reforms were needed in Syria.

"I say openly that we support the idea of states that come from the people, states and governments appointed by the people, not those appointed behind closed doors."

Assad belongs to the minority Alawite sect, a distant offshoot of Shi'ite Islam and his family holds absolute power, commanding the Baath Party and security apparatus.

Baghdad's ties with Iran have improved since the 2003 invasion. Ties with Damascus also have strengthened since last year and the two countries this year signed a trade agreement to ease the transit of goods across their border.

Iraqi Shi'ite leaders are concerned over turmoil in Syria bringing a hardline Sunni leader to power should Assad fall. Last month Maliki warned about regional fallout from a Syrian collapse should there be a change based on sectarian lines.

DEALING WITH PKK

Since the fall of Saddam's regime, some Sunni leaders in the region have talked about a "Shi'ite Crescent" running from Iran through Iraq and Alawite-ruled Syria to Lebanon.

Maliki's government was more openly critical of Sunni Gulf nations military intervention in Bahrain earlier this year to stop protests from mainly Shi'ite demonstrators seeking constitutional reforms from the ruling family.

Maliki also said sending Iraqi troops to the north of Iraq was the best option to push out Kurdish separatist PKK and PJAK guerrillas who have hidden for years in Iraq's mountains, drawing shelling and airstrikes from Turkey and Iran.

"Logic says the way to end their presence, to end the Turkish and Iranian intervention in Iraqi affairs, is sending troops or creating enough Iraqi measures to prevent their presence on Iraqi territory," Maliki said.

"When and how we send them depends on our military capabilities and the nature of our situation, when there will be opportunity we will be there."

Turkey has this year carried out scores of air raids and artillery strikes on northern Iraq's semi-autonomous Kurdish area to hit PKK targets. Ankara has warned it could carry out a cross-border ground attack, depending on talks with Iraq.

Iraq summoned Turkey's ambassador to demand a halt to airstrikes in August after a Turkish strike killed seven Iraqi civilians. PKK guerrillas have stepped up attacks after the collapse in efforts to end their 27-year-old conflict.

(Writing by Patrick Markey)