DUBAI (Reuters) - A leading Bahraini human rights activist said on Monday a court had acquitted him of charges of spreading false news on Twitter after he had been arrested during a protest rally late last year.

Sayed Yousif al-Muhafda, from the Bahrain Centre for Human Rights (BCHR), was released on bail in January after being detained at a demonstration in Manama in December.

Unauthorized rallies and gatherings are banned in Bahrain, which has been in turmoil since pro-democracy protests led by its Shi'ite Muslim majority erupted in 2011.

"The court acquitted me today, but I had spent a month in jail," Muhafda told Reuters by telephone from Geneva.

"We call on the Bahraini government to stop targeting human rights activists and release the head of the centre Nabeel Rajab."

A prominent opposition and human rights activist, Rajab was sentenced to three years in prison last August for taking part in unlicensed anti-government protests.

Bahrain, where the U.S. Navy's Fifth Fleet is based, has stepped up efforts to stamp out the unrest in recent months and several activists have been arrested or jailed for organizing or taking part in unlicensed protests.

Earlier this month rights activist Zainab al-Khawaja was sentenced to three months in jail for insulting a public employee after an appeal court overturned her earlier acquittal.

Muhafda was detained in November for a week on charges of taking part in an illegal gathering and an unauthorized march.

Bahrain's ruling Al-Khalifa family, who are Sunni Muslims, used martial law and help from Gulf neighbors to put down 2011's uprising, but unrest has since resumed.

The opposition says little progress has been made towards its demands for reforms including a parliament with full powers to legislate and form governments. Many Shi'ites complain of political and economic marginalization, a charge Bahrain denies.

(Reporting by Mahmoud Habboush; Editing by Yara Bayoumy and Angus MacSwan)