In a surprise move, parliament president Martin Schulz decided to postpone a vote on the EU-US trade negotiations, known as TTIP.
Then MEPs narrowly voted to postpone a debate on TTIP.
UKIP leader and MEP Nigel Farage said the EU was "running scared" of public anxiety about TTIP. The Greens also said the EU establishment was "scared".
"What is the EP [European Parliament] establishment scared of? Democracy? Citizens' concerns being raised?," the Greens group tweeted.
Mr Schulz postponed the vote because more than 200 amendments had been tabled to a wide-ranging package of recommendations on TTIP.
Those recommendations would feed in to the European Commission's negotiations with US trade officials.
TTIP stands for Transatlantic Trade and Investment Partnership. The European Commission estimates that by 2027 it could boost the size of the EU economy by €120bn (£94bn; $152bn) - equal to 0.5% of GDP.
A summit statement from the G7 leaders on Monday said "we will immediately accelerate work on all TTIP issues". The leaders of the major industrialised democracies hope to get a TTIP deal before the US presidential election in November 2016.
One of the thorniest TTIP issues is investor protection. There is widespread opposition to commercial arbitration panels, called Investor-State Dispute Settlement (ISDS), where firms can sue national governments.
Sections of the centre-left Socialist (S&D) bloc took a tougher line on ISDS than the group's main negotiator, Bernd Lange.
There have been big anti-TTIP demonstrations in Belgium, Germany and some other parts of Europe. Critics say TTIP could weaken EU rules on working conditions and health services.
Mr Lange said he would use the postponement to "work towards reaching a stable majority for the TTIP resolution".
The recommendations now go back to the parliament's trade committee for redrafting. It is due to meet again next week.
Deep divisions have surfaced in the European Parliament over the EU's planned trade deal with the US.