BAGHDAD -- After a week of fighting, Iraqi forces claim they're closing in on Tikrit. On Tuesday they seized the town of Alam, just 5 miles from the city.

General Saad Maan of Iraq's Interior Ministry CBS News

"Now we are surrounding Tikrit from four directions," said General Saad Maan of Iraq's Interior Ministry.

Maan dismissed criticism from America's top general - Martin Dempsey - of Iraqi forces' lack of readiness.

"We are not kids in our work," Maan told me. "We have skills, we have a very big amount of experience."

But in Tikrit, progress is painfully slow, as ISIS fights back with weapons including mines and suicide bombs. A video on the internet appears to shows an Iraqi soldier sobbing for his fallen comrades after an ISIS truck bomb killed several of them.

An Iraqi soldier appears to grieve near his fallen comrade at the hands of ISIS

In the bloody battle for Tikrit, the Iraqi government denies that troops from neighboring Iran are fighting alongside its soldiers and says Iranian officers are serving only as advisers.

"If there is a disaster in Iraq of course it will affect Iran," said General Maan.

But if they retake Tikrit -- it may be a perfect crucible for Iraq's deadly religious tensions to explode. The Iranians are Shiite Muslims -- as are most of the Iraqi forces -- yet Tikrit is a mainly Sunni Muslim city.

"There is no problem. We -- all of us -- are Iraqi," Maan told me. "There is no problem. Believe me there is no problem."

But Shiite Muslim militias are already accused of massacring more than 70 unarmed Sunni men in January after defeating ISIS in Diyala province. The Iraqi government says it is investigating what happened.