Less well known is that his power extends little beyond Bogota; that left-wing guerrillas and right-wing paramilitary groups control large chunks of the country; and that he has been unable to stem horrific human rights violations by his security forces. He has also been the target of corruption allegations, mainly against his wife, Ana Milena Munoz, and his brother, Juan Carlos Gaviria, accused of enriching themselves at the state's expense. But the allegations smack of pre-campaign dirt before spring's presidential elections.
With the 'war on drugs' or the 'guerrilla war' as the perfect excuses, given added credence by the discreet presence of US anti-narcotics agents, Colombia's armed forces, police and intelligence agents have felt free to remove 'troublesome elements' - often opposition politicians, union leaders or peasants with left-wing views. Their task has been made easier by the State of Internal Commotion, the 1991 constitution's version of a state of siege, which has made Colombia a virtual military dictatorship since it was invoked last November.
Distinguishing between murder motives is difficult. But Colombian and international human rights groups say 'political' murders far outnumber cocaine-related killings. Colombia's Defender of the People, a kind of human rights ombudsman, reported that since the founding of the opposition Patriotic Union (UP) party in 1985, 777 party activists had been assassinated. More than 100 trade unionists were killed during Mr Gaviria's first year in power.
That is not to say the President condones such activity. According to diplomats in Bogota, he is sincere in his desire to end the violence. But he is often seen as powerless, a figurehead at best, at the mercy of the powerful security forces. Amnesty's latest report said at least 1,000 people had been 'extra-judicially executed by the armed forces, or by paramilitary groups operating with their (the military's) support or acquiescence' last year. Referring to Mr Gaviria's hobbies of rock music, latin dancing and tennis, one Bogota diplomat said recently: 'He has at times tended to rock, rumba and rattle his racket while the military ruled OK.' In addition to the known killings, several politically involved people 'disappear' every week.
According to the Andean Commission of Jurists, during an 18-month period of Mr Gaviria's rule, only 1 per cent of 'politically motivated killings' could be attributed to drug traffickers, while state security forces were responsible for almost half the killings, paramilitary groups nearly one-third and and left-wing guerrillas about one-quarter. Colombian human rights groups also say 300,000 people have become refugees as a result of political violence in the past decade.
One of Mr Gaviria's main aims this week will be to encourage investment. Colombia is trying to diversify, moving away from coffee, not to mention cocaine. A consortium including BP has said there are rich oil reserves in the east of the country. BP is thought to have spent more than pounds 100m on oil exploration last year. But all is not plain sailing.
Left-wing guerrillas of the Revolutionary Armed Forces of Colombia (FARC) and the National Liberation Army (ELN), together now thought to total around 7,000, continue to target oil pipelines. Last week the main Cano-Limon pipeline was blown up twice, spilling the equivalent of at least 5,000 barrels of oil into the jungle in the eastern state of Arauca, close to Venezuela. It was the 20th such attack this year. The state oil company, Ecopotrol, blamed the ELN, whose aim is to discourage foreign investors. The same pipeline was blown up 62 times last year, costing Ecopotrol millions of dollars. Mr Gaviria will need all his persuasive powers to woo new investors. Colombian and foreign firms are known to have paid protection money to the guerrillas, but payment has not always guaranteed peace.
Mr Gaviria's sales pitch will centre on the fact that he has Pablo Escobar, the cocaine baron, running scared. Escobar's escape from a luxurious prison near Medellin a year ago profoundly embarrassed Mr Gaviria as the drug lord strolled out with the collusion of military officers.
Seven of Escobar's relatives were deported from Chile last week and flew to Germany. One of them, Escobar's nephew Nicolas, told reporters his fugitive uncle was 'a man loved by the people. Wherever he goes, he will be offered a plate of food and a bed.' There is some truth in that because Escobar gave free housing to the Medellin poor in the early 1980s. Now it would be a foolish man who refused him a bed. But whether love motivates such hospitality is doubtful.