The Prime Minister has sidestepped questions on whether she would support Sinn Fein taking their Westminster seats to back her Brexit deal.
Theresa May, who was pressed on the issue a number of times during her visit to Belfast, insisted it was a matter for the republican party to decide on.
“What my job is about is showing those MPs who will be voting on December 11 on this deal why it is a good deal for the UK,” she said.
On Monday, Taoiseach Leo Varadkar said if Sinn Fein was not prepared to ditch its abstentionist policy, it should resign its seven seats to allow other MPs to represent its constituents in the House of Commons vote.
Sinn Fein president Mary Lou McDonald, in Belfast on Tuesday to meet the Prime Minister, rejected the notion as “politically illiterate”.
“Ireland won’t be protected at Westminster,” she said.
“Any notion that Sinn Fein MPs could ride in on their chargers and stop Brexit or save Mrs May are politically fanciful – I would go so far as to say politically illiterate.”
“We are abstentionists, we are Irish republicans, we believe as the nationalist people of this island believe, that our decisions are best taken here in our democratic institutions on this island.”
The party’s MPs do not take their seats in Westminster because they refuse to swear an oath of allegiance to the Queen.
Mrs McDonald accused Mr Varadkar of “disrespecting” Sinn Fein’s mandate.
She further noted that his Fine Gael party had chosen to “abstain” from Northern Ireland, having not run in elections north of the border.
Sinn Fein has been broadly supportive of the Prime Minister’s draft deal, describing it as the “bottom line” and “least-worst option” in terms of protecting the economy on the island of Ireland.
On Monday, Mr Varadkar said Sinn Fein’s seven MPs should consider resigning their Westminster seats to give voters in Northern Ireland an opportunity to elect MPs who would take up their seats.
“Sinn Fein is an unusual party in that it isn’t taking up its seats in Westminster for one reason and not taking its seats in Stormont for another,” he added.
“Generally, people who get involved in politics do so because they want to make a difference and they want to use the democratic process to get good outcomes for their citizens.
“If they are not willing to take up their seats because they feel they can’t because they got elected on the basis of abstention, they do have the option now of resigning their seats and allowing people in those constituencies to decide whether or not they want to have a say when this vote comes to Westminster.
“Bear in mind there are 18 MPs in NI, eight of those are in support of what Theresa May is proposing, but seven are abstaining.”