Hungary's hard-line prime minister has suggested that European Union should step up aid to Syria's neighbors in order to stem the flow of refugees from camps there.
Germany's vice chancellor had also stated on Saturday that his nation is "reaching limits."
The 28-nation European Union is divided over how to deal with the influx, with Germany and Austria stressing the right to asylum for war refugees and Hungary in particular arguing that most are economic migrants. Hungary and other eastern nations reject proposed quotas to spread the human tide around the EU.
Hungary plans to start enforcing tougher frontier security on its border with Serbia Tuesday. Asked in an interview with German daily Bild where future arrivals should go, Prime Minister Viktor Orban replied, "to where they came from."
He argued that people coming to Europe from camps in Lebanon, Jordan and Turkey "were safe there" and added: "There is no fundamental right to a better life, only a right to safety and human dignity."
Orban suggested every EU country pay 1 percent extra into the EU budget while reducing other spending by the same amount. He was quoted as saying that would generate 3 billion euros ($3.4 billion) for aid, which could be increased "until the stream of refugees dries up."
Aydan Ozoguz, a senior German government official responsible for immigrant issues, said that "the pace at which people are fleeing from the region is breathtaking."
But "I must say that I find what Mr. Orban is saying extremely cynical, that they're safe there," she said on Germany's rbb-Inforadio. "Everyone who has been following this knows that the food rations there have been halved - one really can't speak of safety."
Ozoguz was cautious about a statement Friday by her country's foreign minister that 40,000 migrants were expected in Germany over the weekend. "We'll have to see whether this figure really comes true," she said.
Federal police in Munich, the main point of arrival in Germany, said 1,650 people arrived there Saturday morning. Spokesman Thomas Gigl said that was more than in recent days, but he couldn't say how many more would arrive.
Some 450,000 migrants have arrived in Germany this year. The country is expecting at least 800,000 in 2015.
German vice chancellor Sigmar Gabriel said Saturday that "Germany sees itself in a situation where we are reaching limits," news agency dpa reported. He added that "the speed is almost more problematic than the number."
Gabriel said it's important to help the region around Syria and talk to Turkey, where people set off in boats for EU member Greece, about how to slow the flow.
Some asylum-seekers are continuing northward from Germany. On Saturday, Danish police said 225 people crossed from Germany during the night and only three applied for asylum in Denmark. The rest were likely headed to Sweden, Norway and Finland.
The situation at Hungary's border with Austria appeared to have eased Saturday, with a highway near the border town of Nickelsdorf reopened after previously being closed due to the flow of asylum-seekers. Police said some 500 people arrived at the border crossing early Saturday and were put on buses to Vienna, but they didn't know how many more would come.
Saudi Arabia, which along with other oil-rich Gulf states has faced suggestions that it should to more to address Syrian refugees' plight, responded by saying that it has taken in about 2.5 million Syrians since fighting began.
The official Saudi Press Agency quoted an unidentified official source at the foreign ministry saying the kingdom does not consider those taken in as refugees and does not house them in camps "order to ensure their dignity and safety."