Two women have been arrested by New York City for their involvement in an alleged conspiracy to build a bomb and wage a "terrorist attack" in the United States.

According to a federal criminal complaint filed in US District Court in Brooklyn, Noelle Velentzas, 28, and Asia Siddiqui, 31, devised a plot to target police, government or military targets based on their "violent jihadist beliefs."

The duo was charged with conspiracy to use weapons of mass destruction against persons or property in the US.

Neither Velentzas, who entered the court wearing a black dress and hijab, nor Siddiqui, in a green T-shirt over black clothing, entered a plea when they appeared before a US magistrate.

The two women were roommates in the New York City borough of Queens. The complaint stated that both of them conducted extensive research on how to build an explosive device and plan to attack a military base or during a police funeral.

Velentzas praised Al Qaeda's September 11, 2001, attacks on the US and considered former Al Qaeda chief Osama bin Laden a hero.

When agents raided their place, they found bomb-building materials including propane gas tanks, soldering tools, pipes, a pressure cooker and fertilizer. The women also supported beheadings of Western journalists and others by IS, the militant group that controls territory in Syria and Iraq. They were also in touch with Al Qaeda members and Tairod Pugh, a US Air Force veteran charged with attempting to aid Islamic State.

The complaint alleged that the two women had been plotting to build a bomb since last summer. The two "carefully studied how to construct an explosive device to launch an attack on the homeland," Brooklyn US attorney Loretta Lynch said in a statement.