BAGHDAD, Sept 25 (Reuters) - One of Iraq's most precious resources -- doctors -- are fleeing the country in increasing numbers, scared off by persistent violence and drawn to safer, better paying jobs abroad, officials say.

A steady trickle of skilled workers has been flowing out of the country since the 2003 invasion, but in the past year, with the sharp rise in assassinations and kidnappings by insurgents, the exodus of doctors has picked up, they say.

"Iraq is like a battlefield, doctors face danger just getting to work because of terrorist acts," said Aakif al-Alusi, a senior member of the Iraqi Doctors' Syndicate, the official medics' register, who worries about the long-term social impact of the medical brain-drain.

"Doctors are neutral people in our society, all sides have to allow them to carry out their duties, but that doesn't happen here," he said, explaining the reasons why doctors are leaving.

The syndicate estimates 1,500 medical professionals -- doctors, nurses, dentists and pharmacists -- have fled in the past year alone, although precise numbers are difficult to obtain. Almost as many left in 2003 and in 2004, Alusi said.

Many have fled to Jordan and other Arab countries, while others have moved to Europe.

Scores have also headed to the northern Kurdish region of Iraq, where there is much less violence and where pay and conditions are far better than in the centre of the country.

"Doctors feel like they give a lot to society, but society often neglects them in response," Alusi said. "That's a major reason why they end up wanting to go elsewhere."

During Saddam Hussein's rule, doctors, who then made around $2 a month, also sought work abroad, not just because of the low salaries but to seek better training and facilities.

After the 2003 invasion that ousted Saddam, conditions initially improved dramatically, with doctors' salaries rising to around $400 a month. The U.S. authorities also promised a massive overhaul of hospital equipment and new medicines.

DESPERATE TO LEAVE

But aside from pay raises, other improvements were slow in coming. Doctors at Yarmouk hospital, one of Baghdad's busiest, which frequently handles dozens of victims from suicide bombs, say they often run out of anaesthetic and other basic needs.

Doctors have even gone on strike at hospitals in Baghdad and Baquba, north of the capital, after Iraqi soldiers overran their clinics, demanding at gunpoint that their men be treated first.

"After the 2003 invasion, new graduates still dream of going abroad if they can find a good opportunity," said Mohammed Salah al-Din, who left medical school in 1999 and is looking to leave.

While graduates are keen to escape Iraq and build a career, senior doctors with established practices, who have become frequent targets for kidnappers and assassins due to their wealth and status, are also desperate to get out.

For Iraqis, the exodus of such skilled members of society is a deep concern. Medicine is a highly regarded profession in Iraq and despite the lack of equipment in many hospitals, patients praise the hard work and dedication of the medics they have.

"Iraqi doctors are good, I consider them among the best and wouldn't want to be treated by anyone else," said Najat al- Azawi, a retired engineer. "But Iraq is no longer a safe place, they have the right to flee like everyone else."

Aqil Wali, who graduated from medical school in Iraq in 1996, is one of those who managed to escape. Having fled Iraq in 1998, he is now in Denmark. He makes around $5,000 a month and is hoping to double that if he becomes a specialist.

After more than four years in Denmark, he can't imagine ever returning to Iraq, saying the security situation alone would make him hesitate "a thousand times".

"The facilities we have here in Denmark do not exist in Iraq, not to mention the regular water supply, electricity and the social aspects that Iraq still doesn't have," he said.

Others, though, say they are committed to Iraq, however hard life gets. "My country needs me," said Athir al-Rewas, 59, a specialist. "I have my own patients. I would need to start from scratch if I went to another country."