David Mundell reappointed as Scottish secretary
The Scottish secretary has insisted it will be "perfectly possible" for the Conservative government to operate despite losing its majority.
But David Mundell said it was inevitable that the government would need to "cut and change its proposals" to win enough support in the Commons.
He highlighted Brexit as an area where it should be possible to build a consensus with other parties.
Mr Mundell was reappointed as Secretary of State for Scotland on Sunday.
He had been the lone Scottish Conservative MP, but the party's success in last week's general election means he now has 12 colleagues in the Commons.
However, the election saw the Conservatives lose their overall majority, with Theresa May now attempting to secure a deal with the Democratic Unionist Party (DUP) that would see its 10 MPs support her minority government.
Mrs May is to meet her party's backbenchers on Monday, with concerns expected to be raised about her leadership style and the talks with the DUP.
She will also meet Scottish Conservative leader Ruth Davidson, who has called for an "open Brexit" that prioritises free trade rather than curbing immigration.
Brexit Secretary David Davis has predicted some parts of the Tory manifesto will now have to be "pruned" in the wake of the election result.
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Labour leader Jeremy Corbyn has accused Mrs May of "squatting" in No 10, telling the BBC's Andrew Marr Show on Sunday that the country "cannot go on with a period of great instability".
Speaking to the BBC's Good Morning Scotland programme, Mr Mundell said the prime minister was working to ensure there was stability in government.
And he said it was right to seek an arrangement with the DUP to ensure "we are not in constant turmoil within the House of Commons".
Mr Mundell said: "I think it is perfectly possible to operate as a minority government, but inevitably if you are doing that you do have to cut and change your proposals so that they can command support."
Mr Mundell, who became the UK's first openly-gay Conservative Cabinet secretary when he came out in January 2015, said he would like to see the DUP change its position on LGBTI issues.
Northern Ireland is the only part of the British Isles where same-sex marriage remains outlawed.
The DUP has repeatedly used a controversial Stormont voting mechanism - the petition of concern - to prevent the legalisation of same-sex marriage despite a majority of MLAs supporting the move at the last vote.
Mr Mundell said next week's Queen's Speech - which is expected to be delayed for a few days - would set out proposals the government wants to take forward, but added: "What the government is actually able to take forward will depend on what the votes are in the House of Commons".
"There are a whole range of issues on which there is agreement and there is plenty of business that can be conducted on which agreement can be reached", the secretary of state said.
"There are issues on which there won't be agreement and if there isn't agreement then they wont be able to go ahead."
There have been suggestions that the result of the election will force the prime minister to seek a "softer" Brexit than the one she had planned.
Speaking ahead of Mrs May's meeting with Ms Davidson, the prime minister's spokesman said it was clear that the UK cannot control its borders if it remains a member of the single market.
Ms Davidson has repeatedly called for the interests of the economy to be given priority over curbing immigration, saying: "It is about making sure that we put free trade at the heart of what it is we seek to achieve as we leave".
She has previously said she wants the UK to have the "largest amount of access" to the single market after Brexit - and there have been suggestions she will use the influence of her party's new MPs to push for what she describes as an "open Brexit".
Mr Mundell said he had always believed it would be possible to build a consensus, particularly in Scotland, for what the Brexit negotiations should achieve.
He also dismissed suggestions Scottish government proposals aimed at keeping Scotland in the single market had been ignored, but has pledged to "forge a much more constructive relationship" with Holyrood in the future.
Mr Mundell said: "I don't want to see the Brexit deal going through the House of Commons with a majority of one - I want to see it go through the House of Commons with support across the parties and that is what I think we should be looking to achieve."
Scotland's first minister, Nicola Sturgeon, has called for a "short pause" in the Brexit process to allow a UK-wide position to be worked out.
She wants the country's devolved governments and major political parties to be involved in the process, and has argued that voters rejected Mrs May's plans for a so-called "hard Brexit" in the election.