* Al-Omar oil field in the hands of Islamic State
* Al Qaeda's Nusra Front withdraws from two towns
* Islamic State strengthens gains across Deir al-Zor (Releads with oil field capture)
By Sylvia Westall
BEIRUT, July 3 (Reuters) - Militants from the Islamic State group seized control of Syria's largest oil field from rival Islamist fighters on Thursday, strengthening its advance across the eastern Deir al-Zor province, an opposition monitoring group said.
The capture of the al-Omar oil field gives Islamic State control of crude reserves which could be useful to its advancing fighters, and underlines how the al Qaeda offshoot has eclipsed its militant rivals by capturing territory and assets across Syria and Iraq in the past few weeks.
It has declared an Islamic 'caliphate' on lands it has seized in both countries, and urged Muslims worldwide to flock there and wage holy war.
The Syrian Observatory for Human Rights said the Islamic State "took leadership" of the oil field from Nusra Front, the official wing of al Qaeda in Syria.
A video posted on the Internet showed a group of armed men dressed in black outside what they said was the entrance to al-Omar oil field.
One fighter said they had not faced any resistance from Nusra Front and that they had captured the field on the fifth day of Ramadan, or Thursday.
"God is greatest and thanks to God. Islamic State! God is greatest!" the men chanted. It was not possible to independently verify the contents of the video.
(See a map on the battle for control in Syria: http://link.reuters.com/xyw32w)
Nusra Front, which had captured the oil field from the Syrian government in November, had claimed to be producing around 10,000 barrels of oil a day from the field, which has a capacity of 75,000.
Syria is not a significant oil producer and has not exported any oil since late 2011, when international sanctions took effect to raise pressure on President Bashar al-Assad.
Before sanctions, Syria exported 370,000 barrels per day, mainly to Europe.
Nusra Front fighters also withdrew from two towns in Deir al-Zor on Thursday, leaving most of the border province under the control of advancing forces of the Islamic State, the Observatory said.
It said the Nusra Front pulled out of Mayadin and Shuhail, the group's regional stronghold, while local tribal fighters had pledged allegiance to the Islamic State, which has also swept through Sunni Muslim provinces in Iraq.
The Observatory, a British-based monitoring group, said the Islamic State, previously called the Islamic State in Iraq and the Levant (ISIL), now controls an area of Syria five times the size of neighbouring Lebanon.
It has followed al Qaeda's hardline ideology, but has alienated Osama bin Laden's successor Ayman al-Zawahri and other Islamists with its extreme violence.
The jihadi group, which claims authority over Muslims worldwide, has seized weapons from arms depots in Syria and Iraq, money from bank vaults in cities it has overrun, and controls other oil fields and farmlands.
In Deir al-Zor province only the regional capital and airport - still held by President Bashar al-Assad's forces - and a few villages remain outside the Islamic State's control, the Observatory said.
Earlier this week the Islamic State seized the town of Albu Kamal on the Iraqi frontier from the Nusra Front, securing both sides of the border crossing. (Additional reporting by Dominic Evans; Editing by Gareth Jones)