Christian evangelical groups in the US are attempting a "cultural colonisation" of Africa, opening offices in numerous countries to promote attacks on homosexuality and abortion, according to an investigation by a liberal thinktank.

American religious organisations are expanding their operations across the continent, lobbying for conservative policies and laws and fanning homophobia, argues the Boston-based Political Research Associates (PRA).

The groups include the American Center for Law and Justice (ACLJ), founded by the televangelist Pat Robertson, which has established bases in Kenya and Zimbabwe.

"The religious right [in effect] claims that human rights activists are neocolonialists out to destroy Africa," the report states. Groups named in it vehemently rejected the claims.

Entitled Colonising African Values: How the US Christian Right is Transforming Sexual Politics in Africa, the study analysed data from seven African countries and employed researchers for several months in Kenya, Malawi, Zambia and Zimbabwe.

It identified three organisations it believes are aggressively targeting the continent: Robertson's ACLJ, the Catholic group Human Life International and Family Watch International, led by the Mormon activist Sharon Slater.

Each of these "frame their agendas as authentically African, in an effort to brand human rights advocacy as a new colonialism bent on destroying cultural traditions and values", the report says.

In the past five years, the report alleges, all "have launched or

expanded their work in Africa dedicated to promoting their Christian

right worldview. A loose network of rightwing charismatic Christians called the transformation movement joins them in fanning the flames of the culture wars over homosexuality and abortion by backing prominent African campaigners and political leaders."

Dr Kapya Kaoma, an Anglican priest from Zambia and author of the report, said rightwing Christian groups encourage perceptions that same-sex relations are "un-African" and imposed by the west, a view that is in fact based on the Bible that arrived with colonialism rather traditional African culture.

He gave the example of a young lesbian in Zimbabwe who was taken to several churches to have "the devil driven out of her", but later honoured when her grandmother said she was in fact possessed by the spirit of her dead uncle, who had never married.

"The 'foreignness' of homosexuality is not true, but it is when presented in Christian-right language," Kaoma said.

Certain countries are more hospitable to US Christian-right campaigners than others, the research found, in part because of support from government officials.

"The presidents of Zambia, Zimbabwe, and Uganda themselves accused opposition parties of promoting homosexuality to undercut their influence and cater to powerful African religious conservatives."

The ACLJ was invited by Zimbabwe's president, Robert Mugabe, for example, to open offices to train lawyers to work on a constitution that would reflect "Christian values".

A similar effort was made to influence the writing of Kenya's and Zambia's constitutions with the inclusion of phrases such as "life begins at conception".

The report accuses Slater, from Family Watch International, of indulging in alarmist rhetoric that the UN's population control strategy will destroy the African family.

She has claimed homosexuals are significantly more promiscuous and "more likely to engage in paedophilia", it says.

Kaoma said: "[Slater] claims the UN has been taken over by homosexuals. She makes up nonsense and presents it as facts to Africans. She argues that terms such as 'gender rights' and 'sexual identity' are code for homosexuality."

Kaoma believes the American groups are in retreat in the US and so turning to Africa for quick gains.

"They seem to know they are losing the battle in the US, so the best they can do is to be seen to be winning somewhere.

"This gives them a reason to be fundraising in the US. Africa is a pawn in the battle they are fighting at home."

The report was welcomed by gay rights campaigners. Frank Mugisha, executive director of Sexual Minorities in Uganda, said: "I'm grateful for the documentation in the report that confirms that it is homophobia (not homosexuality) that is exported from the west.

"I hope this report serves as a wakeup call for faith communities in Uganda and the west alike to realise that the American culture wars imposed on us by the Christian right threaten not only African culture, but the very lives of LGBTI Africans like me."

Human Life International acknowledged that it has several affiliates in Africa, some of which receive grants, educational materials and other support.

"We feel that it is important for us to be there because the assault on the natural African pro-life and pro-family values is coming from the United States, so we feel obliged to help them understand the threat and respond to it based on their own values and culture," spokesman Stephen Phelan said.

"That is why we can operate with a tiny fraction of the budget that the true colonialists – the extremely well financed population controllers and western governments – operate with.

"We speak to the deep and natural values of our brothers and sisters in Africa, and help them resist the encroachment of very powerful western interests who think that there are too many children in Africa."

He dismissed Political Research Associates' claim that his organisation was practising a new colonialism.

"We expect your more thoughtful readers to note the irony in PRA's argument. Powerful western governments and very wealthy NGOs spend billions annually to stop Africans from having children, to change African laws to be more accommodating to this population control, all in an effort to make them culturally more like the west.

"And the PRA, a proponent of this effort, is accusing a small group of Christian organisations, who together spend a tiny fraction of the development industry's annual budget to preserve pro-life and pro-family natural African values, of 'colonialism'. Where does one begin?"

Slater also attacked the report. "We have no offices in Africa as Mr Kaoma falsely claims," she said. "To make such a fundamental error is alone an indication of the unreliability of his entire report."

She added: "We are not the religious Christian right as Mr Kaoma has insisted on portraying us, despite what I told him and despite the content of our materials published and on our website.

"The only mention of religion on our website or in any of our materials is our concern that religious freedom be protected, regardless of the faith that might be under attack.

"Our position here is based on the clear data that shows a high correlation between religious observance and stable families, and not due to any particular belief or doctrine."

Joy Mdivo, executive director of the East African Centre for Law and Justice, said the US division pays for office space and salaries, but the EACLJ raises its own funds for activities.

"Someone was saying we were given money by the Americans to spread homophobia, and I was telling them, 'I don't have to spread homophobia. Just take a walk down the street, hold another man and look like you are being romantic. I don't have to tell anyone what to do.' That's just the reality of where we are."

• This article was amended on 24 July 2012 to correct the wording of a phrase about the expansion of three organisations' work in Africa to that used in the final version of the report.