Margaret Thatcher claimed the Irish did not have a "highly professional police force" and that she had "failed" in a row over the border.
According to state papers released in Dublin, Taoiseach Charles Haughey launched an impassioned defence of An Garda Siochana after Mrs Thatcher questioned the force's competence.
Mrs Thatcher said she wanted better training of the Garda with international forces as an urgent part of the Anglo-Irish Agreement.
A June 28 meeting between Mr Haughey and the Conservative leader saw her raise major concerns over Garda competence in the wake of the alarming upsurge in IRA violence in Northern Ireland and its success in smuggling weapons and explosives from Libya.
The seizure by French authorities of the Eksund complete with 120 tonnes of Libyan weapons and Semtex explosives prompted the Taoiseach to personally write to France's Jacques Chirac with Ireland's thanks.
However, Mrs Thatcher was not impressed with the Irish police, complaining: "We do not get intelligence from the gardai. They are not the most highly professional force.
"We deal with the Amsterdam and the French police and the Brussels police. Each of them is highly professional.
"Israel is a small country yet it has one of the best police forces in the world.
"The IRA is not an amateur organisation."
Mrs Thatcher said that while she understood Ireland's reluctance to allow gardai to undergo specialist counter-terrorism training in the UK, such training was available in other countries.
"Will you not consider better training for your gardai?" she asked. "I understand if you do not want to use our facilities - I spoke with (Canadian Prime Minister) Brian Mulrooney while I was in Toronto and discussed the matter with him.
"I am not concerned about where they get the training as long as they get it."
However, Mr Haughey defended the Garda's record and said that, unlike the RUC, it patrolled right up to the border.
He also said the Garda had successes in identifying IRA arms dumps and was in the process of trying to infiltrate the Provos in the Louth area.
Mr Haughey said other police forces at times compared less favourably to the Garda.
"We called in the help of the Dutch police in connection with an art robbery some time ago in which there was a Provo involvement - they made a complete mess of it."
However, Mrs Thatcher was adamant that she wanted better security and intelligence liaison between police forces.
She also queried how, when the Irish Government wanted, specific republican targets could be pursued relentlessly.
"You got (Border Fox Dessie) O'Hare alright when you wanted him," she said. "You went after him in no uncertain manner."
Mr Haughey countered by insisting that O'Hare had "rampaged about the country for a week before he was caught".