Talks between UK Prime Minister Theresa May's Conservatives and Northern Ireland's Democratic Unionist Party (DUP) on a deal to support May's minority government are going well and will continue on Tuesday, a senior Conservative source said.

May met DUP leader Arlene Foster at Downing Street earlier on Tuesday. The pair left separately, with May going to parliament for the election of the House of Commons speaker. 

"They (the talks) are ongoing, it hasn't broken up for the day. I'm not putting any timescale on when it will be done," the source told Reuters. "They are going well."

After the Conservatives unexpectedly lost their majority in parliament in last Thursday's snap general election, May hopes to secure a deal to prop up her minority government.

Prime Minister Theresa May leaves 10 Downing Street following a meeting with the leadership of the Democratic Unionist Party (DUP). / CFP Photo

The disastrous election result, which has caused political turmoil in the UK ahead of the beginning of crucial Brexit talks, prompted calls for May's resignation, leading her to apologise to her own MPs on Monday evening. 

"I got us into this mess, and I'm going to get us out," she said. 

Falling eight seats short of retaining its parliamentary majority, the Conservative party is hoping to top up the numbers by forming an informal alliance with the DUP, which won 10 seats.

May is due to travel to Paris later on Tuesday to meet with French President Emmanuel Macron but a representative for her Conservatives will continue the DUP talks.

(With contribution from Reuters and AFP)