The presidency has asked parliament not to send the bill for his assent until legal challenges against it are dealt with.
The speaker has condemned the presidency’s move as “contemptuous”.
The bill criminalises gay relationships and anyone who supports them.
President Nana Akufo-Addo is under intense pressure from those Ghanaians who want him to sign it into law, and also from Western donors and human rights groups who are urging him not to approve it.
A lawyer has challenged the bill at the Supreme Court, saying there was not a quorum – the required minimum number of MPs – in parliament when it was passed.
In a letter to parliament on Monday, presidential secretary Nana Asante Bediatuo said that it was “improper” for the president to receive the bill until the court makes a decision on the matter.
Then on Wednesday, Speaker of Parliament Alban Bagbin halted the approval of new ministers and their deputies, apparently to increase pressure on the president.
“The president’s refusal to accept the transmission of the bill is, by all accounts, not supported by the constitutional and statutory provisions that guide our legislative process,” Mr Bagbin told MPs.
He said parliament could not approve new ministers, saying that the “ongoing scenario poses a grave threat to our legislative authority”.
President Akufo-Addo last month nominated 12 ministers and deputy ministers in a sweeping cabinet reshuffle that saw the finance minister sacked.
Minority leader in parliament Cassiel Ato Forson supported Mr Bagbin’s move, saying the speaker’s concern was legitimate.
However, parliamentary majority leader Alexander Afenyo-Markin said the speaker’s decision was “disappointing” and “strange”, and there should have been wider consultation first.
The main opposition presidential candidate in December polls, John Mahama, has described the letter from the presidency as unconstitutional. He said the presidential secretary had no authority to write such a letter to parliament.
The proposed tough new legislation – The Proper Human Sexual Rights and Ghanaian Family Values bill – was backed by both of Ghana’s main political parties.
It imposes a jail term of up to three years for anyone identifying as LGBTQ+ and five years for promoting their activities.
It has been backed by influential Christian and Muslim leaders.
President Akufo-Addo had previously said that he would sign it if the majority of Ghanaians wanted him to do so.
But he is now seeking to assure the international community that Ghana is committed to upholding human rights.
Ghana’s finance ministry said the country could lose a total of $3.8bn (£3bn) in World Bank funding over the next five to six years because of the bill.
The West African country is suffering a major economic crisis and last year had a bailout from the International Monetary Fund (IMF).
It is unlikely that the Supreme Court will rule on the case before presidential and parliamentary elections due in December.
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