Islamic State militants have targeted the Iraqi capital Baghdad with a wave of devastating car bombs and mortar attacks, killing at least 150 people since Sunday, in an escalating campaign of violence and mayhem.

Four car bombs hit Shia districts of Baghdad on Thursday afternoon. At least 36 people were killed and 98 wounded within the space of two hours, Iraqi officials said. The deadliest attack took place when two parked car bombs exploded simultaneously in the northern Dolaie neighbourhood, killing 14 civilians.

In the eastern suburb of Talibiyah, a suicide bomber rammed his car into a police checkpoint, killing at least 12 people, they added. The dead included seven policemen and five civilians.

These latest attacks follow a series of dramatic advances in Iraq by Isis fighters, who have succeeded in capturing most of the sprawling Anbar province to the west of Baghdad.

In recent weeks the jihadists have taken control of the city of Hit, and have attacked the provincial capital of Ramadi, 70 miles west of Baghdad. Iraqi government troops have fallen back to an air base in the desert outside Hit.

Isis has comprehensively consolidated its grip on the Sunni area, which borders Syria, Jordan, Saudi Arabia and the governorate of Baghdad.

Isis fighters are now encamped on the outskirts of the capital, and appear to be able to target important installations with relative ease. Earlier this month four mortar shells rocked the Green Zone in the heart of Baghdad, home to the US embassy and numerous government buildings.

The jihadists have also fired off mortars at the Shia northern district of Kadhimiya. On Tuesday night they succeeded in killing a member of parliament.

Western observers say Isis is putting pressure on the government of Haider al-Abadi, Iraq’s new prime minister. They do not believe Baghdad is in imminent danger of falling to Isis – or at least not yet. “Baghdad was always the target. You can rampage in Mosul and take vast swaths of Anbar. The taking of Anbar was just to set up a platform to move on Baghdad,” Toby Dodge, director of the Middle East centre at LSE, said. “Isis has strategy and it has tactics. The strategy is to take Baghdad. The tactic is to press on the weakest spots.”

After capturing Mosul, Iraq’s second city, and others areas in early summer Isis fighters surged towards the capital. They paused this operation in July and August, when the Iraqi army and Shia militias staged a concerted fightback.

Isis was now renewing its offensive, Dodge suggested. “They have extended networks in Baghdad. Clearly it was only a matter of time before they went back to their main target. But this isn’t the Battle for Baghdad.”

US and allied air strikes had made little difference, he added, with Isis “quickly adapting”.

Fighting continued in the northern Syrian town of Kobani, where Kurdish units said there was little sign of an Isis retreat. Some reports said Isis had abandoned parts of the territory it occupied after taking heavy casualties.

Speaking from inside Kobani, Ismet Sheikh Hasan, a commander with the main Kurdish militia defending the town, said: “On Wednesday night they started again, coming at us with a lot of strength. Whoever said Isis is retreating is wrong. They are still here in Kaniya Kurda [east] and on the region of Mistenur Hill. There are a lot of them here. They are using a lot of mortars still.” Gunfire could be heard down the phone line.

Isis has besieged Kobani for 31 days. Kurdish fighters from the YPG, the People’s Protection Unit, have partially stayed their advance with the help of US air strikes. In the last two days, US-led coalition forces have conducted more than 40 air strikes against Isis in the area surrounding Kobani – a huge increase from when the air strikes began a fortnight ago.

Sources close to the Kurdish forces who are monitoring the battle said on Thursday that in a month of fighting about 1,290 Isis militants have been killed, compared with only 189 from the YPG-led forces inside Kobani. In response to this bombardment Isis has moved back to villages on the outskirts of the city to the south and west of Kobani.

The black flag of Isis raised more than a week ago on a hill in the city’s east had gone, but Hasan said Isis still had control of the area and are using the homes for cover from the strikes. “The flag is down but Isis still has that area,” he said. “The air strikes are helping but Isis is separating out and going into the houses in the area to protect themselves.”

He said the only area where they have really pushed Isis back is in the west, where the YPG has regained control of a village close to the city. “We took it and now we are fighting for another one, further west.”

Despite the persistence of Isis, Hasan says he does believe the militants might eventually be forced to retreat. “If I didn’t believe this then I wouldn’t be here fighting,” he said.

At least four fighters with the women’s arm of the YPG – known as the Women’s Protection Unit or YPJ – were killed and buried in Turkey on Tuesday after dying from their injuries in the Turkish hospital across the border.

Hasan said the women had a special psychological power against Isis. “Isis thinks that if a woman kills one of them, he cannot go to Paradise. He will go to hell. So the Kurdish women from Kobani want to fight Isis very much. They are very willing. And they are very proud. We are sad that they have died. But all the women who fight right now are here because they want to fight.”