Al-Sharqiyah said the TV crew consisted of Musab al-Azzawi, the Mosul bureau chief, the son of Sunni legislator Mohammed al-Azzawi and Ahmed Salim and Ihab Ma'ad, both cameramen, and Kidar Suleman, a driver.
"Al-Sharqiyah mourns the death of its employees, who were killed by the dark forces trying to ruin security in Iraq, gag freedom of speech and who are chasing the independent and patriotic media," a statement said.
"The four employees were doing their duty while filming Futurqum Alena in the afternoon when they were kidnapped. The gunmen later killed them."
Futurqum Alena is a popular programme during the Muslim holy fasting month of Ramadan, when journalists visit families and share an iftar meal to break the dawn-to-dusk fast.
The channel later gives gifts to the hosts.
The head of Iraqi security operations in Mosul and surrounding Nineveh province, Major-General Riyadh Jalal Tawfiq, who has himself survived more than one assassination attempt in Mosul, said Iraqi forces were pursuing suspects.
"We surrounded the area, chased the suspects and so far we've arrested two of them in a car," he told Sharqiya in an interview.
But he added that two others were still at large.
Al-Qaeda and other groups still roam Mosul, which is struggling to shake off an armed rebellion as the rest of Iraq enjoys better security.
Iraqi journalists have been regularly attacked by al-Qaeda fighters, Sunni and Shia operatives.
Several journalists have also been killed or wounded in crossfire.
According to the Iraqi Journalism Freedom Observatory, the main organisation for the defence of media workers' rights in Iraq, at least 235 media workers have been killed since the US-led invasion of March 2003.
In amother attack, a bomb concealed in a kiosk selling ice-cream killed four people and wounded nine others at a security checkpoint in Baghdad, the capital, Iraqi officials said on Saturday.
Northeast of Baghdad, six Kurdish troops were also killed in a roadside bombing.