It was announced at the weekend that mosques and other places of worship can open for individual prayer from June 15.
But Faith Minister Lord (Stephen) Greenhalgh said communal prayer could not take place until July 4 at the earliest.
When asked on Tuesday when communal worship could return, Lord Greenhalgh told the Religion Media Centre's (RMC) Zoom briefing: "The earliest possible moment would be at step three which is July 4.
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"We need to recognise that some form of collective or public worship is happening pretty much everywhere else apart from the United Kingdom and I think we just need to be ready by July 4, in terms of having the guidance ready to go."
Leeds Council of Mosques said the decision to reopen places of worship for private prayer does not "go far enough" in recognising the practises of the Muslim community, many of which are centred around congregational prayers.
The body urged the city's mosques to remain closed, warning that opening for individual prayer from June 15 would cause "significant challenges" for Mosques and Imams in Leeds.
In a statement, a spokesperson for Leeds Council of Mosques said: "The government's announcement to open places of worship from June 15 for individual prayer is welcome.
"But the decision does not go far enough in recognising the religious practices of the Muslim community.
"Mosques are first and foremost used for congregational prayers. Jama'at/congregational prayers even with a small group of people, following social distancing and other preventative measures, will not be allowed in mosques from June 15.
"Accordingly, opening the mosques from June 15 will cause significant challenges for Mosques and Imams as the expectation from the community will be to resume communal worship (Jama'at) for the public.
"The Leeds Council of Mosques' strong advice is for mosques to remain closed until congregational prayers are allowed.
"Covid-19 is still present and poses a threat to life, with higher cases within BAME communities, and therefore appropriate steps must be taken to minimise risk to health when our mosques do open."
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