Some MPs have suggested Britain will need more time to negotiate its exit to avoid crashing out of the European Union without a deal.
But Mrs. May has insisted the departure date will not change, writing in the Telegraph that she would "deliver Brexit on time".
The Prime Minister is due to report back to Parliament on her negotiations with the European Union on February 13, with a further series of votes by MPs expected the following day.
He added that Britain's only path to avoiding a so-called "hard Brexit", in which London exited automatically on March 29 with no transitional arrangements in place to ensure the continued flow of goods, medicines and transport links, was to accept the existing deal.More news: Kyle Kuzma (hip) will start Thursday's game for Lakers
The vote by British MPs this week to seek "alternative arrangements" to the backstop has caused "disappointment and dismay" in Ireland and Europe, Mr Coveney said, but he stated there have been no "credible" alternatives put forward as yet.
She said she is armed with a "fresh mandate, new ideas, and a renewed determination". The lower house had rejected the withdrawal agreement in the middle of January, and last week, for a Change of the Backstops voted.
"Are they really saying that they would rather not negotiate and end up in a "no-deal" position?"
The move, first reported on Saturday by Sky News, was confirmed by the company in a letter to workers Sunday.
May's office denied a report in two Sunday newspapers that her advisors were considering a June election.More news: U.S. unemployment rate rises to 4 pct in January
May called an unexpected election at short notice in 2017, after which she lost her Conservative Party's small majority and had to rely on support from Northern Ireland's Democratic Unionist Party to continue to govern.
"The last thing this country needs is a general election, I think the people would never forgive us for it, I think what they want is this parliament to deliver Brexit in an orderly way", interior minister Sajid Javid told BBC TV.
On a visit to Stoke-on-Trent on Saturday, he said: "I don't think any MP will sell their votes in that way - that sort of bribery and corruption". How to handle the border between Northern Ireland and Ireland is one of the Brexit dilemmas.
Germany's Foreign Minister, Heiko Maas, said on Sunday that the idea of the United Kingdom avoiding Brexit was unlikely. "There is a deal on the table, and walking away from it will have serious consequences for us all".More news: Are Kylie Jenner and Travis Scott Thinking About Baby No. 2?