4 October 2014 Last updated at 01:38 
Mr Serra and his partner Maria Herrera were found dead at their home on Wednesday night in Caracas.
President Nicolas Maduro and other government officials joined a procession that accompanied the coffins through the streets of Caracas.
Mr Maduro has blamed “ultra-right” opposition groups in the country and in neighbouring Colombia for the murder.
Mr Serra and Ms Herrera were reported to be have been stabbed.
They were buried at a local cemetery after a brief religious ceremony, attended by Mr Maduro.
In tears, Mr Maduro sang the national anthem and songs praising the Bolivarian Revolution – the movement launched in the 1990s by late President Hugo Chavez.
“I know this cemetery very well, because there are Venezuelan martyrs resting in every corner of it,” said Mr Maduro at the cemetery.
“The crowds have been calling for justice. Rest assured that we will, sooner rather than later, arrest those who committed this crime. They have been identified.
“But, more importantly, we will identify the masterminds of these murders. They are abroad, in Colombia and in Miami,” said Mr Maduro.
‘Political murder’Earlier, thousands of people queued up outside the National Assembly building to pay their respects.
Mr Serra was 23 when he was first elected to the National Assembly 
Thousands of people accompanied the coffins through the streets of Caracas Mr Serra, 27, was the youngest member of the National Assembly and was seen a rising star in the governing United Socialist Party (PSUV).
Venezuela has one of the highest murder rates in the world, but the Venezuelan authorities have said Mr Serra was the victim of a political crime.
“This is a political murder, committed to intimidate other young people and try to keep them away from politics,” said Diosdado Cabello, president of the National Assembly.
The Venezuelan government has declared three days of national mourning.
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Venezuelan lawmaker Serra buried
