Galarza is suspected to be the leader of the Gulf Cartel in the border city of Reynosa, a major point for smuggling cocaine into the US.
Suspected members of the Zetas, the paramilitary arm of the Gulf Cartel, hung a series of banners along the roads in the Pacific coast resorts of Acapulco and Zihuatanejo on Saturday, accusing federal officials of protecting a rival cartel.
Near Mexico City, 11 policemen were shot to death in about half a dozen drug-related attacks over three days, prosecutors said on Sunday.
Alberto Bazbaz, the Mexico state prosecutor, said police had arrested 10 people suspected of links to the killings, which occurred on highways and police checkpoints on the outskirts of the capital.
War on drugs
Mexico has seen mixed results this week in its fight against drug gangs.
The latest violence followed the resignation on Saturday of Gerardo Garay as acting federal police commissioner, after one of his aides was accused of working for a leading drug cartel.
Garay had taken the post only in May when the acting police chief at the time was murdered.
Last weekend, security forces arrested Edoardo Arellano Felix, a drug gang leader, after a shootout in the border city of Tijuana. Felix was one of the most wanted international traffickers in the US.
Then on Monday, details were released of two senior Mexican anti-drug officials being arrested for taking bribes to leak intelligence to a drug trafficking cartel.
'More killings'
So far this year around 4,000 people have been killed in Mexico in drug-related attacks, many severely tortured or decapitated.
Al Jazeera's Franc Contreras, reporting from Mexico City, said there was an expectation of more killings ahead.
The president was trying to convince people that the government was doing everything it could, but there was increasing concern that people's day-to-day lives could really be threatened, our correspondent said.