BEIRUT -- Rebels from Syria’s Islamist factions now control large parts of three contiguous provinces in north and eastern Syria, and they are working to install civil administrations there in line with their ambitions of establishing an Islamic state after the fall of President Bashar Assad.

The rebels, from Ahrar al Sham, one of the largest anti-Assad armed groups, and Jabhat al Nusra, a faction that the United States claims is part of the terrorist group al Qaida in Iraq, took over the capital of Raqqa province last week and now also are in control of major parts of Hasaka and Deir al Zour provinces.

“We are running bakeries, because we are the largest group” in Raqqa, said Abu Majd al Shami, a member of Ahrar al Sham, which has branches across Syria.

Ahrar al Sham and Nusra, which is also known as the Nusra Front, have become key to rebel victories in the past year, especially in eastern Syria, and both are competing with other groups to win over the people in areas they have taken over from government troops. Neither recognizes the Supreme Military Command, the rebel umbrella group led by defected Gen. Salim Idriss and the organization the United States and other Western countries have said they will support with training and possibly weapons.

In a video posted by rebels to YouTube after capturing government buildings in Raqqa, where they detained the province’s governor, a rebel commander attributed the taking of Raqqa to the mujahedeen, or holy warriors, rather than the Free Syrian Army, the term generally used to describe groups associated with the secular military command.

Al Shami said that the Syrian air force had continued to bomb the city with a single plane daily and that the area also had been targeted with surface-to-surface missiles. But he said the three positions government troops still maintain in the province were surrounded.

Last week’s takeover of Raqqa provided evidence of executions by rebel forces, also posted to YouTube. Amnesty International, the United Nations and other groups repeatedly have found rebel groups guilty of summary executions, while stressing that the Syrian government’s crimes are far worse in terms of scale and their systematic nature.

Further south, in the province of Deir al Zour, Jabhat al Nusra has held military parades, including one in Mayadeen that reportedly sparked anti-Nusra demonstrations. Nusra also has declared the establishment of a religious court to administer the area north of the Euphrates River, commonly referred to as Jazeera, which means, in English, island. Government military positions still exist, but rebels appear to be isolating them and are closing in on the military airport near the provincial capital.

In Hasaka province, which is east of Raqqa and north of Deir al Zour, fighters from Nusra and other groups recently seized a border crossing at Yaarabia, driving Syrian soldiers to seek safe haven in Iraq. Those soldiers were later ambushed and killed inside Iraq by fighters from the Islamic State of Iraq, the umbrella group for al Qaida in Iraq, in what Iraqi officials have called the most sophisticated military attack on their soil in years.

The rebels’ ties to Iraq in Hasaka are particularly strong. Sinjar, an Iraqi town not far from the Syrian border, has long served as a transit point for smuggling between the two countries.