Theresa May congratulated the Irish people on their decision in the abortion referendum amid pressure to liberalise the strict laws in Northern Ireland.
Ministers - including within her own Cabinet - have indicated their support for liberalisation of laws to resolve an "anomaly" within the British Isles.
Scores of MPs across the Commons have indicated they are prepared to act to rewrite the current legislation given the absence of a devolved administration in Stormont.
But the Prime Minister faces a political headache over calls to act because her fragile administration depends on the support of the 10 Democratic Unionist Party MPs - who strongly oppose any reform to Northern Ireland's strict laws.
And Westminster intervening in a devolved issue could also lead to wider concerns about the political situation in Northern Ireland.
In a post on Twitter, Mrs May said: "The Irish Referendum yesterday was an impressive show of democracy which delivered a clear and unambiguous result.
"I congratulate the Irish people on their decision and all of #Together4Yes on their successful campaign."
Downing Street is understood to believe that any reform in Northern Ireland "is an issue for Northern Ireland".
"It shows one of the important reasons we need a functioning executive back up and running," a source said.
But in a sign of the pressure from within Mrs May's own party, Education Minister Anne Milton suggesting she would back liberalisation if there was a free vote.
The current situation "does feel anomalous", she told ITV's Peston on Sunday.
Cabinet minister Penny Mordaunt - who is responsible for the women and equalities brief in Government - said the referendum signalled a "historic and great day for Ireland" and a "hopeful one for Northern Ireland".
"That hope must be met," she added.
Former women and equalities minister Justine Greening said: "It's clear it's now time for debate and action to achieve the rights for NI women that we have as women across the rest of the UK."
Sarah Wollaston, the Tory chairwoman of the Commons Health Select Committee, said: "I would vote to support an extension of abortion rights to all women across the whole UK.
"As this is a devolved issue, if an amendment is not accepted by the Speaker, then there should at very least be a referendum in Northern Ireland on this issue."
But Justice Minister Rory Stewart warned against the Commons intervening on the issue.
He told BBC's Sunday Politics the UK Government was acting as a "caretaker" administration in the absence of Stormont, and "that must not be used to make fundamental constitutional, ethical changes on behalf of the people in Northern Ireland".
DUP MP Ian Paisley said Northern Ireland "should not be bullied into accepting abortion on demand".
"The settled will of the people has been to afford protections to the unborn life and protect the life of the mother," he said.
Labour MP Stella Creasy claimed more than 140 parliamentarians had already signalled support for an effort to change the law in Northern Ireland.
In a message to the DUP, she said the people of Northern Ireland "consistently support change" in the abortion law and it was "time to put them, not power in Westminster, first".
The forthcoming Domestic Abuse Bill promised by ministers could be used as a vehicle for MPs hoping to change the law in Northern Ireland.
Abortions are currently only legal in Northern Ireland if the life or mental health of the mother is at risk.
Shadow health secretary Jonathan Ashworth said he would back reform of Northern Ireland's strict abortion laws in a free vote, but did not promise Labour would bring a bill before the Commons if the party was in charge.
Women should have the same rights as those elsewhere in the UK, he told Sky's Ridge on Sunday, but stressed Labour must "tread sensitively and be aware of the realities of devolution".