The phrase "contending factions" is correct and usable in written English.
You can use it to refer to two or more opposing political, social, or religious groups that are vying for power. For example, "The election was a bitter fight between the contending factions of the conservative and liberal parties."
In many cases Irenaeus acted as mediator between various contending factions.
An utter lack of trust among the contending factions has hampered all efforts to build a coalition.
The new king began his reign with futile efforts to mediate between the contending factions of the Riksdag.
A nation departing from strict neutrality by giving assistance to one of the contending factions in a war may still be considered a nonbelligerent under certain circumstances.
Doctrinally conservative but personally sensitive and humane, he has been able to empathise with all the contending factions in the church's battles over touchstone issues.
On the pope's death the Colonna recovered their lands and influence, and for many years subsequently Rome was harassed by their struggle for power with the Orsini, which divided the nobility into two contending factions.
The country's forbidding landscape of deserts and mountains has laid many imperial ambitions to rest, as has the tireless resistance of its fiercely independent peoples so independent that the country has failed to coalesce into a nation but has instead long endured as a patchwork of contending ethnic factions and ever-shifting alliances.
His willingness to accept the office reflects his emergence as an acknowledged leader of one of the two political factions contending for control of the state.
Government officials, however, characterized the conflict as a dispute between two Buddhist factions, contending that the action was taken because the abbot of the monastery wanted the Nhat Hanh group to leave.
The White House has asserted it has the authority to name its own interim director, all but assuring a tussle at the Wall Street watchdog on Monday with two separate factions contending they run the agency.
Different factions contended, short- and long-term interests were entrenched in mutual loathing.
