BEIRUT, Lebanon — Islamist rebels and extremist groups have seized control of most of Syria’s oil and gas resources, a rare generator of cash in the country’s war-battered economy, and are now using the proceeds to underwrite their fights against one another as well as President Bashar al-Assad, American officials say.

While the oil and gas fields are in serious decline, control of them has bolstered the fortunes of the Islamic State of Iraq and Syria, or ISIS, and the Nusra Front, both of which are offshoots of Al Qaeda. The Islamic State of Iraq and Syria is even selling fuel to the Assad government, lending weight to allegations by opposition leaders that it is secretly working with Damascus to weaken the other rebel groups and discourage international support for their cause.

Although there is no clear evidence of direct tactical coordination between the group and Mr. Assad, American officials say that his government has facilitated the group’s rise not only by purchasing its oil but by exempting some of its headquarters from the airstrikes that have tormented other rebel groups.

The Nusra Front and other groups are providing fuel to the government, too, in exchange for electricity and relief from airstrikes, according to opposition activists in Syria’s oil regions.