Italian Prime Minister Paolo Gentiloni has said conditions are not right to push through a bill giving citizenship to the children of immigrants.
The law would make some 800,000 people citizens and has already taken years to reach the upper house, or Senate.
Right-wing parties hailed the prime minister's delay but migrant groups said they were bitterly disappointed.
Meanwhile Luxembourg has warned that EU funds may be helping to drive migrants into Libyan "concentration camps".
Responding to an Italian plea for help, the EU has been helping to train Libyan coastguards.
Luxembourg's Foreign Minister Jean Asselborn said "we have financed these coastguards and it's right", but migrants were being rescued in Libyan territorial waters and "can only be taken back to Libya, but back to these camps we've seen pictures of.
"Those are sometimes concentration camps, camps where people are raped, where there is no law."
More than 88,000 migrants have crossed the Mediterranean to Italy so far this year, and more than a quarter of them arrived in June alone.
The numbers are higher than in the first half of last year.
EU action on Libya
Italy has EU backing for a code of conduct that would regulate non-governmental organisations (NGOs) involved in rescuing migrants off the Libyan coast. Critics accuse NGOs of encouraging departures of migrants from Libya.
EU foreign ministers say they have agreed to restrict exports to Libya of dinghies, outboard motors and other goods when there are grounds to believe they will be used by people smugglers. The restrictions will not apply to Libyan civilians such as fishermen whose business is legal, an EU statement said.
Prime Minister Gentiloni called Italy's draft law on citizenship "just", but said he had run out of time and was putting it back until autumn.
He singled out problems with deadlines on the Senate calendar, but his main problem has been in securing political support when the migrant crisis is such a hot issue in Italy.
Many of the new arrivals have come through Sicily, and when a local prefect on the island sent 50 migrants to a hotel in the village of Sinagra at the weekend, dozens of local mayors began a protest outside.
They argued that the facilities were insufficient and the number was far higher than the government's agreement with local authorities to aim for 2.5 migrants per 1,000 of population. "We aren't racist, or against migrants but the distribution has to to be fair," said local mayor Vincenzo Lionetto Civa.
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Migrant issue a hazard for Italian government
By Julian Miglierini, BBC News, Rome
For the normally meek Paolo Gentiloni, the U-turn on this bill that would have extended citizenship rights to the children of long-term immigrants has been quite dramatic – but not entirely surprising.
It had become obvious that a Senate debate would have sparked an internal conflict within his coalition and put his government's survival at risk.
It has also revealed how in the current political climate in Italy, anything related to the issue of migration can become politically toxic.
With migrant arrivals solidly above last year's numbers, the right-wing Northern League and the populist Five Star Movement have strongly increased anti-immigrant rhetoric in the last few months.
Migration is likely to dominate the agenda ahead of the next general election, expected in early 2018.
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What is Italy proposing?
Many European countries already grant citizenship to the children of migrants born on their territory, although the terms vary considerably.
Italy's centre-left-led coalition is planning to offer citizenship to children either born in Italy or those who arrive before they are 12 and spend five years in formal education.
The controversial "ius soli" (right of soil) has taken years to reach Italy's upper house of parliament and when it arrived in the Senate it became the focus of thousands of amendments aimed at halting its path.
It is currently difficult for immigrants to obtain Italian citizenship without an Italian parent.
However, the number of people becoming Italian citizens has nonetheless been on the increase – 201,501 people acquired Italian citizenship in 2016 alone.
Northern League leader Matteo Salvini said more than 7,000 migrants had arrived on Italy's southern shores this weekend alone, adding that the Sicilian mayors' protest was proof that people had had enough.