Iraq’s special forces have been working to fully clear neighbourhoods on Mosul’s eastern edge of Islamic State militants as suspected Isis bombings killed at least 20 people elsewhere around the country.

The current phase and slower pace highlight the challenges ahead for Iraqi forces as they press into more populated areas deeper inside Mosul – where the civilian presence means they will not be able to rely as much on airstrikes.

“There are a lot of civilians and we are trying to protect them,” said Lt Col Muhanad al-Timimi. “This is one of the hardest battles that we have faced till now.”

Some civilians are fleeing the combat zone, while Isis militants are holding others back for use as human shields, making it harder for Iraqi commanders on the ground to get approval for requests for US-led coalition airstrikes. Iraq’s special forces are some of the country’s best troops, but they still largely rely on air support to clear terrain.

Iraqi forces first entered the eastern edge of the city on Tuesday. On Friday, forces began pushing into Mosul proper, but so far have only advanced just over a mile into the city. On the city’s southern front Iraqi forces are still around 12 miles from the city centre.

The extremists captured the city in 2014, and have had plenty of time to erect fortifications. Trenches and berms have turned the streets and alleyways of a neighbourhood once named after the former Iraqi leader Saddam Hussein into a maze, and concrete blast walls have blocked off access to other areas.

“Daesh dug trenches that they filled with water and they have a lot of suicide attackers and car bombs,” said Timimi, using the Arabic acronym for Isis.

Isis fought back on Saturday, pushing the special forces from the southern edge of the Gogjali neighbourhood, where the troops had made their first major foray into the city itself after more than two weeks of fighting in its rural outskirts.

Both sides fired mortar rounds and automatic weapons, while the Iraqi troops also responded with artillery. Snipers duelled from rooftops in residential areas, where most buildings are just two storeys high.

Meanwhile, suspected Isis militants struck far from the frontlines with a pair of bombings that killed at least 20 people. One suicide attack against Shia pilgrims north of Baghdad killed at least 11 people.

The spokesman for Salahuddin province, Ali al-Hamdani, said the deadliest attack had taken place in the city of Samarra, 60 miles north of Baghdad, where a revered Shia shrine is located.

Hamdani said the bomber had parked an ambulance laden with explosives in a car park, and walked up to pilgrims who had just left their buses and were heading to the shrine about 500 metres away. He detonated explosives in the vehicle and then blew himself up.

Hamdani said at least four Iranians were among the dead. Up to 100 others were wounded, he said.

During rush hour on Sunday morning, another suicide attacker rammed an explosives-laden car into a checkpoint outside Salahuddin’s provincial capital, Tikrit, killing at least nine people. Hamdani said five female students, a woman and three policemen were killed in the attack, while 25 others were wounded.

No group has claimed responsibility for the attacks, but they bore the hallmarks of Isis, which has conducted and claimed dozens of similar bombings.