MEXICO CITY, April 28 (Reuters) - Mexico's Senate approved a bill on Tuesday decriminalizing possession of small amounts of narcotics for personal use, in order to free resources to fight violent drug cartels.

The bill, proposed by conservative President Felipe Calderon, would make it legal to carry up to 5 grams (0.18 ounces) of marijuana, 500 milligrams (0.018 ounces) of cocaine and tiny quantities of other drugs such as heroin and methamphetamines.

Mexico's Congress passed a similar proposal in 2006 but the bill was vetoed by Calderon's predecessor Vicente Fox, under pressure from the United States, which said it would increase drug abuse, but now is worried by the drug-related violence along its border.

Calderon has staked his presidency on curtailing the escalating violence between rival drug gangs as they fight over smuggling routes to the United States, with violence spilling into U.S. cities like Phoenix and Tucson.

Calderon was praised by U.S. President Barack Obama this month for his army crackdown in a visit to the Mexican capital and Washington is sending more agents to its side of the border to curb the flow of guns and cash to the cartels.

Drug violence has killed 2,000 people this year across Mexico after 6,300 deaths in 2008.

The bill, which needs to be approved by the lower house, also allows Mexican states to convict small-time drug dealers, no longer making it a federal crime to peddle drugs. Drug dealers are rarely convicted in Mexico as federal courts are saturated with bigger cases and local judges cannot interfere.

Mexico's Congress convenes for a final session before its recess on Thursday but may call an extraordinary session given the outbreak of deadly swine flu in the country that has forced lawmakers to hold sessions behind closed doors to prevent further contagion. (Reporting by Miguel Angel Gutierrez, editing by Patricia Zengerle)