Tánaiste Joan Burton has said there is no "upper limit" on the number of refugees Ireland will take.
Speaking on Newstalk radio on Sunday, Ms Burton said she did not want to put a figure on the numbers of refugees and migrants because it is an evolving situation.
“Ireland has to and will step up to the plate,” said Ms Burton. “As a country that is what we have always done.
“The Government has had a number of detailed discussions, particularly the decision to send the navy and the decision to accept whatever number we are asked to accept.”
Asked what the figure would be, Ms Burton said it would be “the figure that we need to take”.
“It could be 5,000, I wouldn’t like to put an upper limit on it.”
The Tánaiste said the Office of Public Works are examining empty properties where the refugees could be housed.
Fianna Fáil spokesman on Foreign Affairs Brendan Smith called on the Government to continue working with the UN and European partners to assist, not only refugees in the EU, but also the millions of refugees in Lebanon, Turkey, Jordan and Iraq.
"Accepting additional refugees into Ireland must be a priority, but we must also remember that many refugees are living in appalling and freighting conditions in the Middle East with little chance of travelling to Europe, " said Mr Smith. "There are upwards of 4 million Syrian refugees alone in countries neighbouring Syria. Many of these people are living in perilous conditions and need immediate humanitarian assistance."
Convoys head to Hungary
Thousands of migrants streamed into Germany on Sunday, many travelling through Austria from Hungary where they had been stranded against their will for days, while European Union governments argue over how to respond.
A convoy of around 140 cars and vans filled with food and water left Vienna to collect exhausted migrants, many from Syria, who had set out to walk the 170 km stretch through the rain from Hungary’s capital Budapest to the Austrian border, from where many would continue onto Germany.
Onlookers clapped and chanted, “Say it loud, say it clear, refugees are welcome here,” as volunteers loaded their vehicles with food, water and soft toys.
A total of 6,800 migrants entered Germany on Saturday with another 5,000 expected on Sunday, Bavarian state officials said.
Germany has said it expects 800,000 refugees and migrants this year and urged other EU members to open their doors. But others say the focus should be on tackling the violence in the Middle East that has caused them to flee their homes.
The numbers in Europe are small compared to several million refugees in Syria’s neighbours Lebanon, Turkey and Jordan and Pope Francis called on Sunday for every European parish and religious community to take in one migrant family each.
But a poll in France’s Aujourd’hui en France newspaper showed 55 per cent of French people are opposed to softening rules for migrants to access refugee status.
A dozen or so well-wishers offering chocolate and bananas greeted between 600 and 700 people, mostly from Syria, arriving on two trains arriving in the southern German city of Munich, early in the morning with between 600 and 700 people. A third was expected with about 450 people, an regional administration spokeswoman said.
Most were bussed to reception centres after given medical checks, food and clean clothing. Many said they were from Syria, while others were from Afghanistan or Iraq.
Off to Germany
In Hungary, migrants freely boarded trains at Keleti station in Budapest, following handwritten signs in Arabic directing people to trains to Hegyeshalom on the border with Austria. Volunteers handed out food and clothing to hundreds of migrants filling the station.
Around 4,000 crossed into Austria from Hungary on Sunday, the Austrian police said. More than 10,000 have left Hungary since the border was thrown open on Saturday after thousands spent days camping outside the station.
Hungary deployed more than 100 buses overnight on Saturday to take to Austria thousands of migrants who had streamed into the country after northward journeys through the Balkans from Greece.
Austria said it had agreed with Germany to allow the migrants access, waiving asylum rules that require migrants to register in the first EU country they reach.
“We’re happy. We’ll go to Germany,” said a Syrian man who gave his name as Mohammed; Europe’s biggest and most affluent economy was the favoured destination of most.
Hungary, the main entry point into Europe’s borderless Schengen zone for migrants, has taken a hard line, vowing to seal its southern frontier with a new, high fence by September 15th.
Hungarian officials have portrayed the crisis as a defence of Europe’s prosperity, identity and “Christian values” against an influx of mainly Muslim migrants.
Ships to Athens
German Interior Ministry spokesman Harald Neymanns said Berlin’s decision to open its borders to Syrians was an exceptional case for humanitarian reasons. He said Europe’s so-called Dublin rules, which require people to apply for asylum in the first EU country they enter, had not been suspended.
At an EU foreign ministers’ meeting in Luxembourg on Saturday, the usual diplomatic conviviality unravelled as they failed to agree on any practical steps out of the crisis. Ministers are especially at odds over proposals for country-by-country quotas to take in asylum seekers.
The flow of people risking the dangerous journey on flimsy boats across the Mediterranean, and baton-wielding police on Balkan borders, shows no sign of abating, as they flee a four-year-old civil war in Syria that has killed about 250,000 civilians and wars in Iraq, Afghanistan and in parts of Africa.
On the Greek Island of Lesbos, about 500 Afghans protesting at lengthy identification procedures scuffled with Greek police in the main port. A Greek ferry took 1,744 migrants and refugees to Athens from Lesbos on Sunday and another one with 2,500 migrants was expected later in the day, the coastguard said.
A record 50,000 people hit Greek shores in July alone, and were ferried from islands unable to cope to the mainland by a government in financial crisis and keen to dispatch them into Macedonia, from where they enter Serbia and then Hungary.
More than 2,000 have died at sea so far this year.
The Irish Naval Patrol ship LÉ Niamh rescued 329 refugees and migrants on Saturday in the Mediterranean north of Tripoli in Libya.
Additional reporting from Agencies