Ramadi, the capital of Anbar, is one of a dwindling number of areas in the province where pro-government forces still hold ground, and its loss would be a major blow for Baghdad.
Deputy provincial council chief Faleh al-Essawi said security forces attacked IS jihadists in three different areas of Ramadi today and repelled an assault by the militants from the city's north.
A police major said an IS attack from the western side of Ramadi was also held off by security forces and allied tribesmen.
Essawi reiterated that foreign support will be needed to retake the city, saying Iraqi forces can not do it on their own.
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But top cleric Grand Ayatollah Ali al-Sistani, who commands enormous respect among Iraq's Shiite majority, said that Iraqis themselves must take primary responsibility for defeating IS.
"It is wrong that some imagine that the solution is relying mainly on others to protect the country," Sistani said, in remarks read by his spokesman at Friday prayers.
Also today, security forces backed by air support launched "an operation to liberate areas north of the city of Tikrit," said Ali Mussa, an adviser to the governor of Salaheddin province where the operation was taking place.
The city was seized on June 11 during a sweeping IS offensive that overran large areas of the country.
An army lieutenant colonel said security forces were moving slowly toward the militant-held Baiji district because of booby-traps, and they were also advancing west of Tikrit.