LAGOS (Reuters) - Nigeria's president has ordered an investigation into allegations by a rights group of rapes by soldiers and police of women and girls fleeing the Islamist militant group Boko Haram.

Human Rights Watch said in a statement published on Monday that 43 cases of "sexual abuse, including rape and exploitation", had been documented by its researchers in July. A police spokesman flatly rejected the report.

The women and girls were housed at seven camps in Maiduguri, the capital of Borno state, for people displaced by Boko Haram's seven-year-old insurgency, the rights group said.

The Islamist campaign has driven more than two million people from their homes and killed some 15,000 in Nigeria's northeast.

The rights group said it was also told of abuse carried out by camp leaders employed by authorities and members of local militias set up to help the military fight the insurgents.

Nigeria's President Muhammadu Buhari was "worried and shocked" by the allegations, his spokesman Garba Shehu said in a statement on Monday.

"President Buhari has instructed the inspector general of police and the state governors of the affected states to immediately commence investigations into the issue."

Four people told HRW they had been drugged and raped. Thirty-seven said they had been coerced into sex through false promises of marriage and material and financial assistance.

A 17-year-old girl said she was raped by a policeman.

"One day he demanded to have sex with me. I refused but he forced me," she said. She said he threatened to shoot and kill her when she discovered she was pregnant.

A 16-year-old who fled an attack on Baga, near Lake Chad, said she was drugged and raped in May 2015 by a local militia member in charge of distributing aid in a camp.

"There are no reported cases of infractions of law by policemen on or off duty," Don Awunah, a spokesman for Nigeria's national police force, said on Monday in response to the allegations.

An army spokesman declined to comment on allegations related to soldiers and referred the matter to the defense ministry. A spokesman for the department could not be reached by phone and did not respond to a text message.

Boko Haram, which controlled a swathe of land in the northeast around the size of Belgium early last year, has largely been pushed back to its base in the northeast's vast Sambisa forest in recent months.

(Reporting by Alexis Akwagyiram; Editing by Andrew Roche)