The attack, described by Kurdish media outlet K24 as a “bombardment”, hit the tourist resort of Zahko, a popular destination for Iraqis from across the country.
A graphic video of the scene showed screaming women and children, some bloodied by injuries in a cloud of dust in the aftermath of the explosion, echoing a similar attack in January last year that injured two children and was also captured on camera.
Mr Al Kadhimi called the attack “blatant and flagrant violation of Iraqi sovereignty and the lives and security of Iraqi citizens”, and said Baghdad reserves the “full right” to respond to such attacks, the report said.
Turkey rebutted claims that it had carried out the strike that killed eight tourists and wounded another 23 people, saying the attack was a terror act.
The Iraqi military said Mr Al Kadhimi was sending senior government officials to investigate the bombing.
Military spokesman Maj Gen Saad Maan said: "The commander-in-chief of the armed forces dispatched the minister of foreign affairs, the deputy commander of joint operations, his personal secretary and the commander of the Border Guard forces to the place of the bombing to investigate the incident and visit the wounded."
Iraq's Ministry of Foreign Affairs called the attack a "flagrant violation of Iraq's sovereignty and a clear threat to the security of civilians, a number of whom were martyred and others were injured as a result of this act", the state-linked Iraqi News Agency reported. The ministry said the issue would be raised with the UN Security Council.
Turkey's Ministry of Foreign Affairs issued a statement extending its condolences to the family of the dead. It said it was ready to "take all steps to reveal the truth" of who is behind the attack.
A source in Turkey's Defence Ministry said he had "no information reporting or confirming artillery fire in this area", AFP reported.
The defence ministry said two PKK militants had surrendered to a Turkish security point at the Habur border crossing with Iraq, about 10km from Zakho, but made no mention of the attack.
Baghdad on Wednesday recalled its charge d'affaires from Ankara for consultations and summoned the Turkish ambassador for talks after accusing Ankara of the attack.
Iraq's National Security Ministerial Council, chaired by Prime Minister Mustafa Al Kadhimi, also demanded the withdrawal of Turkey's armed forces "from all Iraqi territory".
Riot police were lined up outside the Turkish embassy compound in Baghdad in anticipation of protests against the bombardment, Rudaw said on its English Twitter channel.
The United Nations Assistance Mission for Iraq (Unami) "strongly condemned" the attack, it said in a statement late on Wednesday.
"The mission expresses its deepest condolences to the families of the victims and wishes the injured a speedy recovery," the statement said.
"Civilians are once again suffering the indiscriminate effects of explosive weapons. Under international law, attacks must not be directed at the civilian population.
"Unami therefore calls for a thorough investigation to determine the circumstances surrounding the attack and emphasises that the sovereignty and territorial integrity of the Republic of Iraq must be respected at all times."
Regular military operations
Turkey has conducted regular military operations in northern Iraq, part of a four-decade battle against Kurdish separatist militias, such as the Kurdistan Workers Party, or PKK.
In the past, Turkish operations in Iraq would last for months, but since 2016 Turkey has established a permanent military presence in Bashiqa, about 75 kilometres from Dohuk.
While the Kurdish Regional Government (KRG) is opposed to PKK operations, it maintains strong diplomatic and economic links to Ankara. The separatist PKK has also clashed with Kurdish Peshmerga fighters, a paramilitary force under KRG control, which often co-ordinates with Iraqi government forces.
Continuing Turkish military operations have led to increasing anger from Iraqi nationalist parties in Baghdad and some militia groups linked to Iran, who have in recent months launched attacks against Turkish forces.
In June, a Turkish air strike in the northern Iraqi city of Sinjar killed a 12-year-old boy.
In southern Iraq, there was mounting anger on Wednesday evening as details emerged of the casualties, who were mainly from the south, Zahko mayor Mushir Muhammad Bashir told the Iraqi News Agency.
Basra Today, a popular social media account on Twitter from the southern port city, "called on citizens to set a date for a protest in front of the Turkish Consulate in Basra".