LONDON (Reuters) - President Hassan Rouhani told Iranians on Saturday they could face greater authoritarianism if they replace him with a hardline rival in May's election.

Rouhani was the surprise winner of the last presidential vote, in 2013, after eight years of Mahmoud Ahmadinejad whose re-election for a second term in 2009 caused mass protests and a severe security crackdown.

He now faces serious competition from hardliners, some of whom are close to Iran's supreme leader, Ayatollah Ali Khamenei, who has criticized Rouhani's economic record, saying his detente with the West and concessions on Iran's nuclear work had yet to yield economic benefits.

"We will not let them bring the security and police atmosphere back to the country," Rouhani told a rally in the city of Yazd, according to the semi-official Tasnim news agency.

"Iranians will prove to the world at the May 19 election that the era of violence, extremism and pressures in our country is over and Iran is pursuing the path of reason."

Among Rouhani's challengers are Ebrahim Raisi, an influential cleric with decades of experience in the hardline judiciary, and conservative Tehran Mayor Mohammad Baqer Qalibaf, a former Revolutionary Guards commander.

Raisi, a close ally of Khamenei, was one of four judges who oversaw the execution of thousands of political prisoners in 1988.

Rouhani still retains considerable support, especially among Iran's large bloc of young, urban voters attracted to his vision of greater social freedoms and an end to Islamic clerical interference in their personal lives, analysts say.

However, human rights activists say his administration has achieved little on personal freedoms or freeing political prisoners and has been more focused on reducing Iran's international isolation.

Rouhani said in a televised speech that "freedom is the most important issue for the Iranians" and that he had ordered the intelligence ministry not to "interfere in people's privacy".

(Reporting by Bozorgmehr Sharafedin; Editing by Robin Pomeroy)