Caleb Orozco, fighting to overturn country's anti-gay laws, is said to have faced more threats of violence since start of court case

Death threats against Caleb Orozco, the gay rights campaigner attempting to overturn laws that criminalise homosexuality in Belize, have escalated during the four-day courtroom hearing, his lawyer has claimed.

The high-profile challenge to the Caribbean state's colonial-era "anti-buggery" legislation has stirred up resentment of the gay community, according to Lisa Shoman.

"There has been a visible increase of threats and violence against Mr Orozco and against all homosexuals in Belize," she told the local News 5 TV channel in the capital Belize City.

"There are threats for killing, burning, shooting; you name it. It has to stop. We are all Belizeans. We can agree to disagree without getting violent about it."

The London-based Human Dignity Trust, which is supporting his case as part of its global campaign to decriminalise homosexuality, said Orozco's car had been damaged in an attack on Thursday night.

The country's supreme court is expected to reserve its decision on the legality of section 53 of Belize's criminal code, which outlaws "carnal intercourse" between consenting same-sex adults. The four-day hearing is due to end on Friday afternoon.

Belize's main churches have formally joined the court case, opposing decriminalisation. Bishop Phillip Wright, head of the Anglican community in Belize, said he did not see "homosexual behaviour as consistent with the witness of scripture" but deplored intimidation.

He added: "We do not support any form of violence against persons of a homosexual orientation and we distance ourselves from any such action or tendency in the wider population. After all, the church has to find a way to bring people together and to encourage hatred and that form of bigotry really is not acceptable in our book at all."

In an interview with Channel 5, a local Catholic priest, Ian Taylor, took a different approach, declaring: "Globally it has been determined by states that violence against homosexuals is highest within the homosexual communities itself. First of all the victim syndrome that they tend to portray is actually within the community itself – they are aggressive against each other, and less from those who are considered heterosexual."

In court, the attorney general of Belize, Nigel Hawke, argued that there were no fundamental rights upon which Orozco could rely in the country's constitution. "It is within our right as a sovereign nation to keep section 53 on the books as long as we want," he said. "It is the people's right through their elected officials to change the law."

Orozco's counsel, Chris Hamel-Smith SC, told the supreme court that his client was not seeking new rights but simply wished to enforce existing "fundamental freedoms" governing privacy, human dignity and equal protection under the constitution.

Lord Goldsmith, the former UK attorney general, who represented the Human Dignity Trust and others, told the court that many Commonwealth and other countries had decriminalised same-sex sexual activity, including India, Armenia, the Balkans, New Zealand and Azerbaijan.

"It somewhat ironic," he added, "that so much ink has been spent in characterising my clients as foreigners … when in fact the law they are trying so hard to preserve is a colonial import; it is a legacy of British rule."

Jonathan Cooper, chief executive of the Human Dignity Trust, said: "The Belize judicial system has been a credit to the rule of law. It is therefore deeply regrettable that Caleb has been subjected to such hatred outside the court and on Facebook in particular. Caleb is one of the great human rights defenders of our time. He is a remarkable and brave man. He should be celebrated by the people of Belize, instead of being attacked."