Ali al-Dabbagh, a government spokesman, said a cabinet-level delegation would soon be sent to Mosul.
"The cabinet stressed the need to move quickly to support the security effort with intensive military operations to restore security and order in Mosul and to reassure citizens," he said in a statement.
Prompted by the violence, the Iraqi government has already sent more than 1,000 police personnel to Mosul.
Major-General Ali Ghaidan, commander of Iraqi ground forces, said the fruits of the recent crackdown would soon be visible, attributing the exodus to "media exaggeration that gave rise to fear and horror among these families ... even if no threat was received".
Yunadim Kanna, an Iraqi Christian legislator, said more than 1,500 families had left following recent killings of Christians, but that the situation had calmed in recent days.
"We expect these areas to be controlled, and the families to return to their homes in coming days," he said.
Kanna met Nuri al-Maliki, Iraq's prime minister, a Shia Muslim, along with Christian officials on Monday.
The targeted violence in Mosul has brought renewed attention to the plight of Iraq's Christians, who number in about 800,000 people.
Since the US-led invasion of Iraq in 2003, members of the Christian clergy have been targeted and a number of churches bombed.
The Chaldean Catholic archbishop of Mosul was kidnapped in February and his body was found two weeks later.
Although the Iraqi authorities have yet to publicly announce who they believe is behind the campaign of violence, many believe it is the work of al-Qaeda.
But some Christians have placed the blame on other elements in the city - home to Arabs, Kurds and Turkmen - saying there is a systematic campaign to oust them from the city.
Kanna, like other Christians, said he hinted that there might be government involvement.
"I don't want to accuse anyone, but I am saying that [those carrying out attacks] are wearing police uniforms," he said.
The US has also spoken out against the attacks, with a statement from the embassy saying the killings are the work of "terrorists".