The Europe-wide "day of action" includes dozens of events across several nations with the biggest demonstration expected in London. There are also rival anti-migrant events due to take place, notably in the Czech Republic, Poland and Slovakia.
The biggest mass migration since World War II has divided Europe with Germany pushing for compulsory quotas within the Europe Union but eastern European nations snubbing the proposal.
Pressing his Czech, Hungarian, Polish and Slovakian counterparts at a meeting in Prague, Germany's foreign minister on Friday warned the influx of hundreds of thousands of migrants could be "the biggest challenge for the EU in its history".
"If we are united in describing the situation as such, we should be united that such a challenge is not manageable for a single country," Frank-Walter Steinmeier said, calling for "European solidarity".
The International Organization for Migration said over 430,000 migrants and refugees had crossed the Mediterranean to Europe so far in 2015, with 2,748 dying or going missing en route.
Germany has taken the lion's share, admitting 450,000 refugees so far this year, most of them fleeing violence in the Middle East -- particularly Syria -- and Asia.
But Steinmeier's appeal for EU members to accept proposals to share around 160,000 migrants fell on deaf ears among eastern nations.
Slovak Foreign Minister Miroslav Lajcak said he wanted a solution "that is not imposed" but "made jointly". "Migrants don't want to stay in Slovakia," he added bluntly.
Denmark's right-wing government also said it would not take part in the quota scheme.
With criticism growing of Hungary's treatment of thousands of people passing through on their way to northern Europe, premier Viktor Orban said he wanted 3.0 billion euros ($3.4 billion) handed to Turkey, Lebanon and Jordan, the first ports of call for Syrians trying to escape conflict.
"If it takes more money, we will increase aid until the refugee flows are drying up," Orban told Germany's Bild newspaper.
"These migrants do not come from war zones but from camps (in these border countries), where they were safe.
"They are not fleeing danger -- they have already fled and should not fear for their lives."
They come to Europe not "because they seek safety but because they want a better life than in a camp. They want a German life, perhaps a Swedish life".
Orban's comments come as Hungary builds a fence on the Serbian border to keep migrants out and has adopted tough new laws that will make it a crime to cross the border illegally from next week.
"From September 15, the rules are changing in Hungary, if you cross the border illegally, you will be immediately arrested by the authorities," Orban warned Friday.
Orban insisted on Friday that his country was just trying to apply European rules in seeking to register the new arrivals, pinning the blame on fellow EU member Greece for waving migrants through for onward travel north.
EU lawmakers have called for an international conference on migration, together with the United States, United Nations and Arab countries.
Facing criticism that his government has been too slow to help, US President Barack Obama pledged to admit at least 10,000 Syrian refugees over a year starting October 1.
Underscoring the scale of the crisis, some 7,600 migrants entered Macedonia in just 12 hours overnight, according to a UN official, with more buses on their way from Greece.
From Macedonia, the migrant route cuts through Serbia into Hungary and from there veers west into Austria, from where most of the arrivals continue on to Germany and Sweden.
Germany has placed 4,000 troops on standby for this weekend alone to cope with the influx.
From the smugglers who pack migrants into leaky boats, to taxi drivers who charge exorbitant sums to ferry them across land, some people have sought to profit from the migrants' plight.
The French government on Friday suspended an honorary consul in the Turkish resort of Bodrum after she was secretly filmed selling rubber dinghies and life jackets to desperate refugees.