* New law restricts rules for public protests
* Two people died in recent protests in the capital
By Margarita Antidze
TBILISI, July 1 (Reuters) - Georgia's parliament on Friday increased restrictions on public protests in response to opposition rallies in May in which two people died.
Two people -- a policeman and a demonstrator -- were killed during protests in May when protestors demanded the resignation of pro-western President Mikheil Saakashvili, who came to power in the 2004 elections following the Rose Revolution.
Georgian riot police used teargas, water cannon and rubber bullets on May 26 to halt five days of demonstrations, during which at least 37 people were injured.
The new law says rallies must not come within 20 metres of government buildings, prevents small rallies from blocking roads, railways and highways and prohibits the possession of dangerous objects and the consumption of alcohol by participants.
People under 18 and those who are not Georgian citizens cannot act as organisers of protests. The law also calls for protection of journalists at the rallies.
Saakashvili, whose country fought a brief war against Russia in 2008 over two Kremlin-backed rebel regions, said that recent clashes were a provocation of the "occupiers", a clear reference to Russia, which maintains troops in South Ossetia and Abkhazia.
Political analysts say that as long as the opposition remains fragmented, there was little threat to Saakashvili, 43, whose term is due to end in 2013.
His domestic opponents accuse him of monopolising power since the revolution that overthrew the post-Soviet old guard in the Caucasus state, where pipelines carry oil from the Caspian Sea to the West, skirting Russia. (Editing by Matthew Jones)