At least 28 people have been killed and scores more wounded in bombings targeting a commercial street and an army checkpoint in the Iraqi capital of Baghdad, Iraqi police say.

A car packed with explosives blew up on Thursday in a commercial street of Baghdad al-Jadeeda, an eastern district of Baghdad, killing more than 15 people and wounding more than 50, a police officer said.

Iraqi forces 'indiscriminately bombing and shelling' Fallujah

Separately, a suicide car bomber targeted a main army checkpoint in Taji, just north of Baghdad, killing seven soldiers and wounding more than 20 others, the officer said.

In an online statement, the Islamic State of Iraq and the Levant (ISIL) group claimed responsibility for the attack on the commercial street.

No one has claimed responsibility for the other attack, which comes as Iraqi forces are trying to dislodge ISIL fighters from Fallujah, their stronghold just west of Baghdad.

Up to 90,000 civilians are believed to still be inside Fallujah, according to the United Nations, which had earlier estimated the number to be 50,000.

'Harrowing' situation

Lise Grande, UN humanitarian coordinator for Iraq, said civilians could face a "harrowing" situation in Fallujah, 50km west of the Iraqi capital.

"We have underestimated how many civilians are in Fallujah," she told Reuters news agency.

"People who are coming out are giving us the strong impression that we could be talking about maybe 80,000 to 90,000 civilians that are inside."

Fallujah is a historic bastion of fighters, first the ones who fought against the United States occupation of Iraq in 2003, and then against the Shia-led authorities that took over the country.

Finance Minister Hoshiyar Zebari said last week that he expected the recovery of Fallujah would take time as ISIL had dug tunnels and planted explosive devices in roads and houses to impede the military advance.

Source: Agencies