Under the proposals, 120,000 additional asylum seekers will be distributed among EU nations, with binding quotas.
It comes after a surge of thousands of mainly Syrian migrants pushed north through Europe in recent days.
Mr Juncker told the European Parliament it was "not a time to take fright".
Germany, the main destination for many migrants, supports quotas, but some EU countries oppose a compulsory system.
There were more chaotic scenes on Hungary's southern border with Serbia, with migrants breaking through police lines at the Roszke camp, and forcing the closure of the M5 highway.
France welcomed the first of 1,000 migrants it has pledged to take from Germany, having committed to receive 24,000 migrants over two years.
Conditions were reported to be improving on the Greek holiday island of Lesbos, where thousands of migrants have now been screened and put aboard ferries to Athens in a new government drive.
