Meghan Markle is suing Associated Newspapers, which publishes the Mail on Sunday and Mail Online, for printing parts of her letter to Thomas Markle in August 2018.
The preliminary hearing was held at the High Court in London, with the judge in attendance but lawyers participating remotely because of coronavirus restrictions.
Lawyers for Associated Newspapers sought to strike out parts of the duchess’ claim, in particular that the newspaper was responsible for causing the rift between father and daughter.
The US former actress has alleged her “vulnerable” father was “harassed and humiliated”, “manipulated and exploited” by reporters before the publication.
But Anthony White, representing the organisation, said some of the allegations were irrelevant and had no proper legal basis.
It was “highly unlikely that she has any credible basis for these allegations of impropriety” towards her father, as she has had no contact with him since she got married to Prince Harry in 2018, he said.
The publisher had also not “acted dishonestly” in summarising or editing parts of the correspondence, which was standard practice in media reporting, he added.
Associated Newspapers denies it breached privacy in publishing the letter, and that the letter was edited to change its meaning.
It also facing a claim for copyright infringement and breach of data protection.
The legal action is separate to a claim brought by Prince Harry, who is suing another news organisation for allegedly intercepting voice messages.
Harry has accused sections of the media of waging a “ruthless campaign” against his wife before and after their marriage in a glittering ceremony at Windsor Castle in May 2018.
He has said he feared “history repeating itself” given the treatment of his mother, Diana, princess of Wales, during her lifetime.
Earlier this week, the couple said they would no longer speak to or cooperate with four major British tabloid newspapers, including the Daily Mail, accusing them of “distorted, false and invasive” reporting.
Meghan’s 75-year-old father has said he felt pressured to share the letter after its contents were misrepresented in a magazine article.
Details of communications from the couple to him were revealed in court documents on Monday, in which they urged him in text messages not to speak to the media before their wedding.
Thomas Markle did not attend the marriage, after he allegedly staged paparazzi-style photographs of himself for money.