In a joint statement, Peter Robinson and Martin McGuinness said politicians need to work together to find "an agreed solution".
They said: "We recognise and support the right to peaceful protest but the way forward is through dialogue.
"The current protests are damaging Christmas trade and the local economy as well as disrupting peoples' daily lives.
"An absence of street protests would provide the space to allow us all to work together to find an agreed solution."
The latest in a series of protests saw around 1,000 loyalists demonstrate peacefully in the city centre on Saturday amid a heavy police presence.
Protesters also disrupted rush hour traffic in Belfast last week and more flag protests are being planned this week.
Assistant Chief Constable Dave Jones said police are "determined to do everything we can to ensure people can go about their normal business".
"People have a right to go about their daily lives, to shop and to socialise, to pick up their children on time and get home to their families without being held up by these protests," he said.
"We will continue to have sufficient resources in place to deal with this activity and will endeavour to keep disruption to a minimum. However, I am appealing to those wishing to protest to consider how their actions are affecting the wider community.
"Police remain fully committed to delivering a safe and secure Christmas for everyone. An extensive evidence gathering operation will be put in place and where appropriate people will be brought before the courts."
The vast majority of all communities in Northern Ireland simply want to enjoy the festive period with their friends and families in peace.
PSNI ACC Dave Jones
Glyn Roberts, Chief Executive of the NI Independent Retail Trade Association, also reiterated the call for demonstrations to end.
"These protests have cost the local economy millions of pounds and have put immense pressure on already struggling local retail and hospitality sectors this Christmas," he said.
"We would urge the protestors to listen to the joint call from the First and deputy First Ministers to end the protests and to go into dialogue to resolve this situation.
"Our local economy cannot afford to have roads blocked and town and city centres disrupted in what is the most important trading time of the year."
He added: "In this last week before Christmas, we urge the community to rally round and support local traders and not to be put off shopping in local town and city centres. Your local traders need you at this time and it is quite simply the case that if you don't use them, you will lose them."
On Saturday PUP leader Billy Hutchinson told UTV the process surrounding the removal of the flag earlier this month was "flawed" and "illegal" and suggested it may be possible to challenge the decision to put it back.
Violence erupted following a number of street protests, which have been held across Northern Ireland after councillors voted to only fly the flag on designated days at city hall and not all year round.
Forty people have been arrested so far in connection with the disorder.
Almost 30 police officers have been injured and a number of politicians have been subjected to death threats.
Two peace rallies were held in Belfast at the weekend, with over a thousand people taking part in a 'non-silent' demonstration on Sunday to show "the world that Northern Ireland has moved on from the Troubles".
On Monday, UUP leader Mike Nesbitt met with the Secretary of State for Northern Ireland, Theresa Villiers, and discussed a number of issues.
"I impressed upon the Secretary of State the importance of ending the current piecemeal approach to dealing with the past," he said.
"Given that sectarianism is the toxic legacy of the Troubles, this will be an essential element in creating a truly shared future."