Fierce fighting between Iraqi army forces, backed by helicopter gunships, and the foreign-backed insurgents are reportedly underway in some parts of the town, said Talib Mohammed, the mayor of the town, which is 160 km (100 miles) north of Baghdad.
"Snipers and roadside bombs are preventing the army from totally controlling the town," he added.
The al-Qaeda-linked Islamic State in Iraq and the Levant (ISIL) militants overran parts of Sulaiman Bek earlier this week. Militants raised the black flag of ISIL over parts of the town on Thursday.
The army liberated some parts of the town on Friday.
An army captain in Sulaiman Bek said snipers were hindering bomb disposal teams faced with dozens of explosive devices.
"Our job is not easy, it's a guerrilla war," said Captain Falah Abdul-Ameer. "Snipers are a big issue now. We can't work out their exact location, they shoot and change places."
Prime Minister Nouri al-Maliki visited an army base west of Ramadi on Friday night to meet military commanders and tribal leaders, and discuss army operations, local officials said.
Fighting erupted in Ramadi between the ISIL terrorists and Iraqi security forces backed by local tribesmen early on Saturday, police and local officials said.
RA/MB