The Equality and Human Rights Commission has ruled out holding an investigation "at this stage" into Islamophobia in the Conservative Party.
The move comes after the Tories published terms of reference for an independent probe into discrimination and prejudice within its ranks in December, with Professor Swaran Singh appointed to chair the inquiry.
The EHRC decision comes despite a plea from the Muslim Council of Britain (MCB) for the equalities watchdog to look into Islamophobia in the party after the council submitted a dossier of complaints in March, including allegations against Prime Minister Boris Johnson.
Its general secretary, Harun Khan, has called the terms for the Tory inquiry a "facade" for covering up racism within the party.
A spokesman for the EHRC said it would allow the internal investigation to take its course, but reserved the right to step in if the inquiry is not being carried out to its satisfaction.
"We have given very careful consideration to complaints raised about discrimination and Islamophobia in the Conservative Party," said a spokesman.
"We have concluded, in the light of the decision by the party to institute an independent investigation, that it would not be proportionate to initiate our own investigation at this stage.
"We will be monitoring the review and requiring the party to provide regular updates on progress.
"If we are not satisfied with progress or how the investigation is conducted we will review our decision and do not rule out the use of our legal powers."
The MCB, which represents mosques, schools and charitable associations, has accused the ruling party of attempting to "hide" what it claims are "hundreds of incidences of Islamophobic bigotry" committed by members.
The organisation handed its first document to the EHRC in May last year, providing details of about 150 people it believed had displayed Islamophobia or made anti-Islamic or anti-Muslim comments.
It renewed calls for the watchdog to investigate when it submitted a document in March this year which swelled to include double the number of original claims.
Mr Khan said: "We have previously described the Conservative Party's attitude to Islamophobia as one of denial, dismissal and deceit.
"The publication of the terms of reference for its inquiry reflects that regrettable attitude.
"They are a facade to hide the hundreds of incidences of Islamophobic bigotry we have identified in its ranks.
"In sum, it seems even today, the Conservative Party refuses to acknowledge that there can be bigotry and prejudice directed at Muslims."
In a statement issued on Tuesday, Amanda Milling, co-chairwoman of the party, said Prof Singh would soon start to take evidence after finalising the inquiry's terms.
He will be looking at the nature and extent of complaints, any related complaints of harassment and/or victimisation, and how the party has investigated and dealt with such complaints, the Tories said.
MP Ms Milling said: "The Conservative Party will never stand by when it comes to prejudice and discrimination of any kind. It is why we are committed to this investigation, to ensure that any abuse that is not fit for public life is stamped out."
Prof Singh said: "I'm happy that the terms of reference for the investigation have been agreed and I will now begin work on the next stage of the investigation."
Meanwhile, the EHRC is carrying out an investigation into anti-Semitism within the Labour Party, with results expected later this year.
