* OAS boss Almagro says regime "has become more tyrannical"
* U.S. weighs tougher sanctions after Tillerson tour
* OAS panel due to report on potential rights crimes (Adds comments from OAS rights investigator, new paras 12-18)
By Stephanie Nebehay
GENEVA, Feb 20 (Reuters) - Sanctions should be stepped up against Venezuela's leaders and oil sector in response to the country's repressive political climate, the head of the Organisation of American States (OAS) said on Tuesday.
Under President Nicolas Maduro, "dictatorship has become more tyrannical" and the suffering of its 30 million people has increased amid dire shortages of food and medicine, said Luis Almagro.
"Sanctions have to become harsher, this is the way to move forward. Those against dictatorship should unite," the secretary general of the 34-member OAS told a Geneva human rights forum organised by UN Watch, a non-governmental organisation.
"We must apply sanctions, harsher ones. We must starve the regime financially."
Sanctions have so far focused on individual members of Maduro's government and a ban on buying new Venezuelan debt.
Restrictions on Venezuela's all-important oil industry would represent an escalation of financial pressure on the OPEC member state.
Almagro, asked by Reuters to elaborate on his remarks, later told reporters: "The sanctions should be not only personal sanctions, but sanctions also against the regime itself.
"That makes it necessary of course to target oil production, it makes it necessary to target the family of the dictators, it makes it necessary to target money-laundering."
Maduro will stand for re-election in April in a ballot opposition leaders plan to boycott. Critics say it is a farce, with his main rivals barred from standing and a compliant election body bound to favour the ruling socialists.
Maduro denies the system is undemocratic and calls the OAS a pawn of U.S. policy.
U.S. Secretary of State Rex Tillerson said two weeks ago at the end of a five-nation tour of Latin America that the United States was closer to deciding whether to impose sanctions on Venezuelan oil.
Irwin Cotler, a former Canadian minister of justice serving on an OAS panel investigating alleged crimes against humanity in Venezuela, said it would report its findings next month.
"We heard compelling witness testimony and we received documentary evidence of extrajudicial executions and widespread systematic attacks on civilians as a matter of state policy," Cotler told the forum.
He cited cases of torture, rape, and arbitrary detention.
"We are witnessing a dismantling of democracy, an assault on the rule of law and on the independence of the judiciary," he added.
Rights groups have said than 125 people died in anti-government protests last year.
Venezuelan authorities have previously dismissed reports of such rights abuses as baseless.
Reporting by Stephanie Nebehay; editing by John Stonestreet