Downing Street has said the government will deliver on landmark House of Commons votes extending same-sex marriage and abortion rights to Northern Ireland, indicating Theresa May supports the principles of the backbench amendments, if not their methods.

The prime minister was in the Commons but did not vote on Tuesday night when the amendments to a Northern Ireland bill, tabled by two Labour backbenchers, were passed by resounding majorities, delighting civil liberties groups.

“The government has heard the message the house has delivered, and will seek to act upon it,” a Downing Street source said.

May’s government has resisted efforts to extend the rights of equal marriage and abortion to Northern Ireland, the last place in the UK that does not have them, arguing such matters should only be decided by the devolved assembly and executive.

However, these have been suspended since January 2017 amid a political deadlock that shows no sign of ending. The amendments, tabled by the Labour MPs Stella Creasy and Conor McGinn, were added to a technical government bill connected to the elections and budgets for the devolved government.

The No 10 source said: “There are, we believe, some technical issues with the amendments as they were presented and so what we want to do is try to take forward precisely the spirit of those amendments so that we can act upon the principles that they set out.

“There is also a general principle of devolution, in that it would be better for a reformed Northern Ireland executive to take these issues forward. Clearly, that isn’t the case just at the moment.”

Asked why May had not voted – she voted on other amendments in the session – the source indicated this was because the prime minister was concerned about the implications for devolution, although she agreed with the general ideas.

The source said: “Clearly there are technical issues with the amendments, but she has herself talked about the importance of, anywhere in the United Kingdom, people being able to marry who they love.”

The amendment on equal marriage, tabled by McGinn, a longstanding campaigner on the subject, was passed in the Commons by 383 votes to 73.

McGinn’s amendment will theoretically lead to an automatic change in the law within three months if the devolved government remains stalled, although the Northern Ireland Office has said it might take longer owing to legal practicalities. If and when the region’s executive is revived, it could then approve or repeal the measure.

In a vote a little more than 15 minutes later, MPs approved an amendment by Creasy to extend abortion rights to Northern Ireland by 332 votes to 99.