Cabinet Minister Mathias Cormann says the Turnbull government gave its best shot in convincing Senate crossbenchers to agree to race-hate law changes.

The coalition failed in its attempt to change the words "offend", "insult" and "humiliate" in Section 18C of the Racial Discrimination Act to "harass and intimidate" during a late-night debate on Thursday.

The attempt to re-word the section was killed off by a Labor amendment to the bill, 31 votes to 28.

The government had also sought to tweak the Human Rights Commission's complaints process, but the fate of those changes is still up in the air.

0:00 00:00 / 00:00 Share Share on Twitter

Share on Facebook

RELATED READING 18C protects Muslim criminals, One Nation senator Malcolm Roberts says

Senator Cormann defended the effort to pursue 18C changes despite expectations some crossbenchers would disagree.

"We were very keen to give it our absolute best shot to persuade the crossbench to join us in strengthening anti-vilification laws," he told ABC radio on Friday.

He left questions to the fate of the changes to Attorney-General George Brandis.

Critics dubbed the result a win for multicultural Australia, but Senator Brandis said it was a "sad day" for free speech.

"It is political censorship, pure and simple. A law like that has no place in a free country," he said during the debate.

RELATED READING Australians tweet their experiences with racism after proposal of changes to 18c

Senator Brandis outlined all the "deeply offensive and insulting" instances other senators had called him a white man and said the spirit of the late cartoonist Bill Leak had presided over the debate.

Mr Leak died of a suspected heart attack in March, after coming under fire for a controversial editorial cartoon about indigenous parental neglect.

He was investigated for a possible breach of 18C but the racism complaint was subsequently dropped.

"You talk about freedoms and rights, well people do have a right to take offence when hurtful, hateful comments are made to them because of their race," Indigenous Labor Senator Malarndirri McCarthy told the Senate.

"Australia is not colour blind but in this bill we want to turn a blind eye to racism."

Greens senator Nick McKim said there was an overwhelming case not to change the Racial Discrimination Act.

"We have listened to multicultural Australia. We will stand shoulder to shoulder with them," Senator McKim said.

"They have asked us to support retaining section 18C precisely as it is currently worded."

Labor welcomed the defeat of the 18C changes, saying weakening protections against racial hate speech never made sense.

"This win will be felt by anyone who has experienced racism and knows that racism is more than just words," the party's multicultural spokesman Tony Burke said.

-With AAP.