Monday's claim, corroborated by other rebel groups, underlined the fragmented state of Africa's largest nation.
The two main Darfur rebel groups, which are in peace talks with the government in the Nigerian capital Abuja, denied attacking the Sharif oil pumping station on Saturday.
The government said rebels killed 15 people in the attack but did not affect the 3000 barrels per day (bpd) capacity.
Both groups said the new rebel movement, the Sudanese National Movement for the Eradication of Marginalisation, attacked the small oilfield.
The movement says it is based in the central areas of Sudan and Kordofan, which lies immediately to the east of Darfur.
"This was our first military operation and we chose the oilfields because this is the wealth of Sudan, which this government is not sharing with all of its people," said leader Ali Abd al-Rahim al-Shindy, speaking from an undisclosed position in central Sudan.
Observers say the number of
militias will hinder peace talks
He said the movement supported peace processes to end the Darfur conflict and more than two decades of civil war in Sudan's south.
But it felt other areas such as the east and central Sudan were being left out of these talks, which will decide how to share power and wealth in the country.
Sudan is a budding oil producer with a crude output of about 320,000 bpd. It hopes to raise that to half a million as a new pipeline comes on stream next year.
Plethora of militias
A Western diplomat in Khartoum said the plethora of armed movements in Sudan did not bode well for a southern peace deal - due to be signed by the end of the year - which will usher in a new government.
The United Nations has expressed concern at new movements emerging in Darfur, where four rebel movements are now active.
Only two of them are represented at the talks in Abuja.