The BBC's Laura Trevelyan at UN headquarters in New York says that officials are hoping the ceasefire holds as losing control of Goma would severely undermine their authority throughout the rest of the country.
The Security Council met late on Wednesday and unanimously adopted a non-binding statement which condemned the fighting and called on the Tutsi rebel group CNDP, led by Laurent Nkunda, to "bring its operations to an end".
The council also expressed concern at reports of firing across the Congolese border with Rwanda, echoing comments made by Secretary General Ban Ki-moon earlier in the day.
They urged the governments of the DR Congo and neighbouring Rwanda to "take concrete steps to defuse tensions and to restore stability in the region."
In a statement before the summit, Mr Ban said the intensifying conflict was "creating a humanitarian crisis of catastrophic dimensions and [threatening] dire consequences on a regional scale".
He said the "collapse of discipline" among DR Congo troops was "especially worrying" and appealed to the Congolese government to "spare no effort establishing control over its forces".
UN officials in Goma have said DR Congo soldiers in the city are nervous and out of control and have been firing into the air.
Mr Ban said he deplored the deliberate targeting of civilians and their use as human shields and said UN peacekeepers were "doing everything possible to protect civilians and fulfil their mandate in untenable circumstances".
Correspondents say the 17,000-strong UN force in DR Congo - the world's largest - is stretched to breaking point.
Both Congolese President Joseph Kabila and the head of the UN mission have called for more troops.
Laurent Nkunda urged the government to declare a ceasefire too
The UN meeting did not make a decision on the request but said it was considering it.
In the meantime, peacekeepers from elsewhere in the country would be redeployed to Goma to back up the 800 troops stationed there.
Before the meeting, UK Africa minister Mark Malloch-Brown said the world was mobilising to avoid a repeat of tragedies like the 1994 Rwandan genocide, when the international community looked on as hundreds of thousands were killed.
"We all have those ghosts in the backs of our minds," he told the BBC. "We need to stop this before it escalates to anything like that level."
France, which holds the rotating presidency of the EU, has said that it supported sending forces to the area.
Foreign Minister Bernard Kouchner said that up to 1,500 men could be deployed "in Europe's name within eight to 10 days".
European governments will meet on Monday to discuss the possible deployment of peacekeeping troops.
Earlier on Wednesday, rebel leader General Laurent Nkunda told the BBC he was declaring a ceasefire in Goma and urged government troops to do the same.
Thousands of displaced people have been fleeing rebels
He added that the goal of his forces was to protect his Tutsi community from attack by Rwandan Hutu rebels, some of whom are accused of taking part in the 1994 genocide.
A BBC correspondent in the city says there was a "stampede" as thousands of displaced people poured into Goma on the third day of fierce fighting in the area.
Congolese soldiers withdrawing from the village of Kibumba, 30km (20 miles) to the north, also retreated to the city, creating a sense of panic among the population, our correspondent added.
Earlier in Kibumba, our reporter saw an exchange of fire across the Rwandan border. Rwanda denies claims it is backing the rebels.
A peace deal was signed in Goma between the government and various rebel groups at the end of January.
Although he signed the deal, Gen Nkunda has refused to disarm while Rwandan Hutu rebels still operate in the area.
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