Liberal senator Cory Bernardi says some Liberal Party members have quit over the government’s decision to drop proposed changes to race hate laws.

Liberal Senator Cory Bernardi warns the Abbott government risks further frustrating the party faithful if it doesn’t reconsider its decision to abandon changes to the Racial Discrimination Act.

The controversial South Australian senator will co-sponsor a bill in the Senate to change the Act, despite the government last week dropping its controversial proposal to amend Section 18C.

Senator Bernardi said he had received hundreds of emails from Liberal Party members who were disappointed the government had decided to dump proposed changes without consultation.

Some long-standing members had even quit the party, he said, and he didn’t want further erosion of support as the government struggled to push budget measures through the Senate.

“I don’t want to see the Liberal grassroots start to cast their eyes anywhere else,” he told Network Ten on Sunday.

“They’re frustrated already that the government isn’t able to get through much of its legislative agenda.”

Family First senator Bob Day will introduce a private members bill to amend the Act, vowing he won’t be intimidated against standing up for freedom of speech.

Senator Bernardi said he would support the bill because it was “absolutely consistent” with Liberal Party values and was a sensible proposal to protect free speech.

Religious and cultural groups oppose the 18C changes.

In dropping the proposals, Prime Minister Tony Abbott said said the debate had complicated relations with ethnic groups.

Senator Bernardi said it was disappointing a small group of Australians could “dictate and determine” what was in the national interest.

“We’ve got to manage for mainstream Australia, not for particular groups within it,” he said.

The Liberal backbencher was dumped from a senior coalition role in 2012 for linking homosexuality to bestiality, and separately has suggested the burqa should be banned in Australia.

Senator Bernardi stood by his comments, saying in time people would recognise what he said was “entirely accurate”.