A security source told the BBC that at least 35 soldiers and allied Sunni tribesmen were killed in a series of suicide car bomb attacks.
A senior IS leader was also said to have been killed east of the city.
Government forces have encircled Ramadi and are preparing for a final assault on the city, which IS overran in May.
Last week, troops retook the key western district of Tamim, which is only separated from the city centre by a tributary of the Euphrates, and the headquarters of the Iraqi military's Anbar Operations Command.
On Monday, a senior source in the Anbar Operations Command said IS militants launched a wave of attacks across Ramadi as they tried to regain areas recently recaptured by government forces.
Five suicide bombers drove cars packed with explosives at government positions, including those in the northern district of Albu Farraj, killing more than 20 soldiers and tribesmen, the source added.
At least 15 militants were subsequently killed in a gun battle, before Iraqi and US-led air strikes forced the rest of the attackers to retreat.
A sixth suicide car bomb attack, in south-western Ramadi, killed another 15 soldiers and tribesmen, the source said.
Iraqi media also reported that an IS leader in charge of setting up car bombs had been killed along with four of his aides in a military operation in the Jazirat al-Khalidiya area, 12 miles (20km) east of Ramadi.
Security sources identified the militant as Ibrahim al-Halabi, a Syrian national.
The US military believes there are between 600 and 1,000 IS militants in Ramadi.
It says they have developed a strong defensive system in and around the city, including using improvised explosive devices (IEDs) to create minefields.
Islamic State militants have reportedly launched several counter-attacks in the Iraqi city of Ramadi, which government forces are trying to recapture.