Women from Northern Ireland may be able to have abortions in the Republic of Ireland once new laws are introduced there, the Irish prime minister has said.

Leo Varadkar said he could not see why women would be barred from crossing the border for such procedures when they are already allowed access to healthcare in the Irish Republic.

“We do have people who already come to our hospitals from Northern Ireland for healthcare so I imagine it will be treated as a normal part of our health service,” Varadkar said. But he added that the matter would have to be examined as legislators draft a bill in the coming months.

His comments came as Theresa May said she had no plans to help liberalise abortion rights in Northern Ireland. It will soon be the only part of the two countries where abortion is outlawed in nearly all cases after the Republic of Ireland overwhelmingly backed liberalisation.

Over the weekend, May posted on Twitter: “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.”

But a similar move in Northern Ireland would place at risk her own relations with the socially conservative Democratic Unionist party, with which she struck a deal to stay in power after losing her Commons majority at the last general election.

A No 10 spokesman said that while the prime minister had congratulated Ireland, the UK’s focus was on “restoring a democratically accountable devolved government in Northern Ireland so that locally accountable politicians can make decisions on behalf of the public they represent”.

Hundreds of pro-choice activists vowed to hit Northern Ireland like a “seismic wave” as they stepped up their bid for change with a rally in Belfast on Monday.

Micheál Martin, a member of the opposition Fine Fáil party in the Dáil, called on the country’s government to ensure that women in Northern Ireland could access abortion services in Irish GP surgeries and hospitals, saying it was Ireland’s “obligation and mandate to ensure the passage of this legislation because of the urgency of the issue for many women in our society”. The Sinn Féin leader, Mary Lou McDonald, said the issue was very important as Brexit approached.

Varadkar told the Dáil on Tuesday that the Irish government wanted to legislate for abortion in the country as quickly as possible. But he said it should not be rushed because some people did not accept the referendum result and may legally challenge the legislation. Varadkar said it was likely to be January before parliament would be able to give full effect to the referendum decision.