Indonesian police on Monday questioned a Muslim cleric over a hate speech complaint by a civil group following a lecture in which he said new banknotes carried the communist hammer-and-sickle symbol.

Communism remains a highly sensitive issue in Indonesia after bloody anti-communist purges in the country in 1965 and symbols and some literature remain outlawed.

Habib Rizieq, head of the Islamic Defenders Front (FPI), is being investigated over two separate complaints, as authorities take a tougher stance against fundamentalist groups in the world's largest Muslim-majority nation.

Rizieq made the comments about the banknotes in a videotaped lecture last month.

"This is already a formal investigation," said Jakarta police spokesman Argo Yuwono. "We are looking further into his comments on whether the money has the hammer-and-sickle symbol."

The central bank has denied the new banknotes carry any communist symbols.

"What's being seen by some people as a hammer and sickle symbol is actually the Bank Indonesia logo...and it is part of the security elements in the notes to prevent counterfeiting," Bank Indonesia said in a statement this month.

Last week, Rizieq was questioned by police over claims that he made defamatory comments in 2014 about one of Indonesia's founding fathers, Sukarno, and had questioned the legitimacy of the state ideology, Pancasila.

If found guilty, he could face up to four years in prison.

The cleric has denied wrongdoing in both cases.

Rizieq's supporters condemned the investigation of the complaints as indicating the "criminalization" of their leader.

"This is systematic tyranny against Habib Rizieq, which destroys the pillars of justice," said the FPI's Jakarta chief, Novel Bamukmin. "It's a form of criminalising the clerics."

Rizieq and the FPI were key drivers behind recent rallies against the Christian governor of Jakarta, whom they accused of insulting the Muslim holy book, the Holy Quran. The rallies were the biggest Indonesia has seen in nearly 20 years.

Jakarta governor Basuki Tjahaja Purnama is in on trial for blasphemy, but remains one of the frontrunners in next month's governor election.

Purnama has denied blasphemy. There are concerns he has been unfairly targeted and that the government has not done enough to protect the rights of religious and ethnic minorities.