Stanley Johnson defended his son’s controversial remarks on the burka, which sparked threats of an internal party investigation into the former foreign secretary.
Boris Johnson refused to apologise for comparing women who wear burkas to “letter boxes” or “bank robbers” in a newspaper column last week.
The former cabinet minister said he was against bans on the veils in public places, but added it was “ridiculous” that people chose to wear them.
Critics have claimed the remarks are part of a well-orchestrated attempt to gather support from the right-wing of the Tory Party before a possible autumn leadership bid.
There is mounting speculation that Mr Johnson, whose ambitions are well-known, could set off a leadership contest in a matter of weeks.
However, Stanley Johnson refused to confirm or deny these claims, as LBC host Tom Swarbick challenged him on his son’s potential to become Prime Minister.
Mr Swarbick asked: “This is a yes or no question. Do you think that Boris could still become Prime Minister?”
After a long and awkward pause, Boris’ father simply said: “Pass.”
In his own newspaper column this morning, Stanley Johnson suggested that Boris should have gone further in his remarks.
Writing in The Sunday Telegraph, he said: “Surely, there are circumstances where a ban or appropriate restrictions would be in order.”
Boris Johnson has been seen returning from holiday in Italy following the widespread outrage over his comments.
A growing divide has emerged in the Conservatives over how the party should handle the remark.
A Sunday Express poll revealed a majority of Britons believe Boris Johnson should not be punished for his burka comments.
On Saturday, eurosceptic Tory MP Jacob Rees-Mogg branded the investigation a “show trial”.
The leader of the European Research Group blamed the public outrage around Mr Johnson’s remarks on senior Conservative figures “nervous” about a Boris leadership bid.
He also attacked Theresa May’s feeling of “personal rivalry” with Boris Johnson.