Much of the anger was aimed at leading Leave campaigner, UKIP's Nigel Farage, who was at one point accused of using "Nazi propaganda".
UK Prime Minister David Cameron is to meet European Union leaders for the first time since the UK voted to leave later on Tuesday.
He is stepping down to allow his successor to conduct exit negotiations.
Opening the session at the European Parliament, European Commission chief Jean-Claude Juncker urged the UK to clarify its position on Brexit as soon as possible.
