European leaders have been warned two emergency meetings could be the "last opportunity" to thrash out an effective response to the migrant crisis.
Home Secretary Theresa May is attending talks with her counterparts from other EU states in Brussels today, while David Cameron will meet fellow leaders tomorrow.
The most crucial issue at stake will be whether politicians can resolve disagreements over a plan to relocate 120,000 asylum seekers from Italy, Greece and Hungary.
Britain has vowed not to take part in any resettlement scheme - a position Mrs May reaffirmed again today as she arrived at the meeting.
Calling for new measures to deter "illegal economic migrants" from trying to enter the EU, she said: "We also need as Europe to get on with the job of the wider measures that need to be taken, of ensuring that we are breaking the link for economic migrants between making this dangerous journey and settling in Europe.
"So we need to return those people who are illegal economic migrants and who have no right to be here.
"We need to ensure people arriving at Europe's borders are being properly dealt with, properly fingerprinted, so that decisions can be made and where they are illegal economic migrants they can be returned."
Britain has agreed to resettle 20,000 of the most vulnerable Syrian refugees over the next five years but will take them direct from the refugee camps bordering the country.
Mr Cameron is expected to use tomorrow's summit to urge EU leaders to do more in the region, including tackling people-smuggling gangs.
Ahead of the meetings, the United Nations refugee agency said the situation is becoming "increasingly chaotic and unpredictable" as an average of 6,000 people arrive on European shores every day.
The UNHCR warned that a relocation scheme alone "will not be enough to stabilise the situation".
Spokeswoman Melissa Fleming said: "This may be the last opportunity for a coherent European response to manage a crisis that is increasing suffering and exploitation of refugees and migrants and tension between countries."
She said it is "essential" that the 120,000 additional places are approved this week for any relocation programme to be considered "credible" but claimed that any scheme cannot be effectively implemented without the creation of "adequate reception facilities" in countries where refugees and migrants enter Europe.
The agency also called for strengthened mechanisms for the humane return of those not granted international protection and urgent measures to stabilise the situation, including additional humanitarian funding for countries hosting large refugee populations.
Labour MP Keith Vaz, chairman of the home affairs committee, called for the EU to end "the internal squabbling and bickering which only serves to aggravate the already desperate refugee situation".
He added: "This has become a stain on the history of the continent, and a betrayal of the values of the EU which are based on decency and humanity.
"European governments need to act now to stop this senseless herding of vulnerable people and passing them from country to country."
Charities said a breakthrough is crucial.
John Dalhuisen, Europe director at Amnesty International, said: "Failure is not an option. EU leaders have to show leadership and face the crisis head on, not build more barriers and carry on quibbling over quotas."
Anna Musgrave, of the Refugee Council, said: "The time for talking is over. We need to see concrete action aimed at immediately alleviating suffering and sharing responsibility for protecting refugees across Europe and of course Britain must play its part."