At least 12 other people were taken to hospital, two of whom were in critical condition, said the Centre Hospitalier Universite Laval. Police say the victims were all men between the ages of 39 and 60.
One suspect was arrested at the mosque, where police were called at about 8 p.m. local time, and the other turned himself about an hour later, Quebec City Police Inspector Denis Turcotte said.
Prime Minister Justin Trudeau and Quebec Premier Philippe Couillard both condemned the incident as a terrorist attack.
"This is another senseless act of violence that can not be tolerated", Spicer told the daily briefing Monday as he described the conversation between the two leaders.
We should not be shocked that people would hold negative stereotypes about Muslims, when politicians such as Leitch have implied that Muslims are holders of "anti-Canadian values", who need to be monitored for "barbaric cultural practices" against women.
"Muslim-Canadians are an important part of our national fabric, and these senseless acts have no place in our communities, cities and country", he said.
In June, the same mosque was the target of a hate crime during the Muslim holy month of Ramadan.
Later Monday, Trudeau was to travel to Quebec City, accompanied by his fellow political leaders - a rare show of cross-partisan unity that illustrated the magnitude of the tragedy.
The motive for the attack was not clear.
"Security at our mosque was our major, major concern", Mohamed Labidi, the mosque's vice-president, said Monday. "We must stand together".
Trudeau's statement was made against the backdrop of an executive order signed by US President Donald Trump on Friday, blocking all refugees from coming to the United States for 120 days and suspending entry for citizens from Iran, Iraq, Syria, Yemen, Sudan, Libya and Somalia for 90 days.
Six people were gunned down, with eight more injured, just after Sunday evening prayers at a mosque in Quebec's capital.
Mosques across Canada are under police surveillance, Couillard also said.
New York City Mayor Bill de Blasio also chimed in and said the NYPD would be augmenting its presence around NYC mosques after the attack.
"We're going to put the safety of Americans first, we're not going to wait and react, as I said in the (previous) statement, the president is going to be very proactive in protecting this country", Spicer said.
Over the weekend, Mr Trudeau said Canada would welcome refugees after Mr Trump suspended the U.S. refugee program and temporarily barred citizens from seven Muslim-majority countries from entering the United States.
"The SQ confirms that only [one of the] individuals arrested last night ... is considered to be [a] suspect", Quebec police said, according to a translation.