"Those behind the two death cases have been detained and we have begun preliminary investigations," said Sheikh Rashed bin Abdullah al-Khalifa late Tuesday in a televised address.
The minister apologised for the killing of the two demonstrators in clashes with police on Monday and Tuesday, saying that police should exercise retraint.
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"We regret that the recent events have caused casualties and apologise to the nation, especially to the families of those who died or wounded," he said.
"Over the past years, I have always insisted that security personnel should exercise self-restraint to avoid such regrettable events, and we have succeeded in doing so," he said.
King Hamad in an address on Tuesday expressed sorrow for the deaths, announced a ministerial probe and pledged to press ahead with reforms which he kicked off with a 2001 referendum that restored parliament in 2002 after it was scrapped in 1975.
In the 1990s, the Arab state which faces Iran across the Gulf waterway, was plagued by a wave of Shiite-led unrest that has abated since the 2001 reforms.
Thousands of demonstrators gathered in Pearl Square Tuesday following the funeral of one of the two men. The protest aimed at changing the regime was called for cyber activists.
Inspired by the uprisings of Egypt and Tunisia which led to the ousting of their respective Western-backed leaders, some Bahraini demonstrators said they will stay in the square until they topple the monarchy.
The Shiite-majority Gulf state which is ruled by the Sunni al-Khalifa dynasty is a staunch ally of the United States and home to the US Navy Fifth fleet.
