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 on Tuesday, 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 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.
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.
During her Belfast visit, the prime minister also faced calls to deliver certainty on Brexit as she met business representatives.
Mrs May later urged MPs to act in the national interest in the December 11 vote on her draft withdrawal agreement with the EU. It was a message aimed at her erstwhile DUP allies, whose 10 MPs are pledged to vote against her, and all parliamentarians opposed to the agreement.
The DUP is promising to vote against the draft EU withdrawal deal.
Mrs May said: “I will be talking to my DUP colleagues, as I will be talking to colleagues in the House of Commons and across the House of Commons, of the importance of this vote, for the future of the UK, for the future of jobs for their constituents, for the future security of their constituents, this is a deal that protects those issues but also delivers on the Brexit vote.”