The SNP will "work constructively" with the UK government to find a way forward on Brexit, the party's Westminster leader has pledged.
Ian Blackford was speaking moments after the prime minister survived a confidence vote in the Commons.
All 35 SNP MPs voted in favour of the no confidence motion, which was lodged by Labour leader Jeremy Corbyn.
But Theresa May defeated the attempt to remove her government from power by 325 votes to 306.
She secured the victory after rebel Tory MPs and the DUP - who helped to vote down the prime minister's Brexit deal by a historic margin on Tuesday - backed the government.
Mr Corbyn, whose no confidence motion was backed by all of the opposition parties, argued that Mrs May's "zombie" administration had lost the right to govern.
He also urged Mrs May to "remove clearly, once and for all, the prospect of the catastrophe of a no-deal exit from the EU and all the chaos that would come as a result of that."
Mrs May said she would immediately start individual talks with other parties in an attempt to find a Brexit compromise that MPs will back.
The prime minister said the talks had to be approached with a "constructive spirit" from all sides, adding: "We must find solutions that are negotiable and command sufficient support in this House."
And she pledged to "continue to work to deliver on the solemn promise to the people of this country to deliver on the result of the referendum and leave the European Union".
Welcoming the prime minister's offer, Mr Blackford said: "We have to work together, where we can, to find a way forward and I commit the Scottish National Party to working constructively with the government."
However, he said that delaying Brexit by extending the Article 50 process, holding another EU referendum and avoiding a no-deal Brexit all had to be "on the table".
Mr Blackford added: "We have to agree to enter these talks on the basis that we can move forward and achieve a result which will unify all the nations of the United Kingdom."
After meeting with the prime minister, Mr Blackford tweeted a letter he sent to her outlining the SNP's position and calling for a "real alternative" to the rejected deal.
And in a statement outside 10 Downing Street Mrs May confirmed that she had met with the SNP, Lib Dems and Plaid Cymru but said she was "disappointed" Jeremy Corbyn had chosen not to take part in the discussions.
Mr Corbyn has said that before any "positive discussions" can take place, the prime minister should rule out a no-deal Brexit.
Following my meeting with the Prime Minister, I have written to her outlining the SNP's position. These cross-party talks cannot be about cosmetic changes to her already rejected deal. We must discuss real alternatives and a second referendum must be on the table. pic.twitter.com/Q9XQTlPkmF— Ian Blackford (@IanBlackfordMP) January 16, 2019
However, speaking on BBC Radio's Good Morning Scotland programme, Scottish Secretary David Mundell said taking no-deal off the table was the wrong starting point for negotiations with the EU.
He said: "Well I hope that we will end up in a situation where we're not facing no-deal, but the best way to stop a no-deal is to have a deal.
"The starting point to take no-deal off the table is the wrong starting point. The starting point is let's get a deal that we can agree in parliament, that can command support and that's what the prime minister is seeking to do through the discussions she's having."
Mr Mundell also said holding a second Brexit referendum or so-called People's Vote was not in the best interests of the country.
He added: "Everything is up for discussion, but what isn't going to be an outcome is arrangements that seek to stop Brexit, which I believe the People's Vote is designed to do and not only that, it would be extremely divisive in our country."
Nicola Sturgeon, the Scottish first minister and SNP leader, was in London earlier on Wednesday to meet her party's MPs ahead of the confidence vote.
Ms Sturgeon had a telephone conversation with Mrs May on Tuesday evening, when she urged the prime minister to "stop the clock" on the Brexit process.
The UK is currently due to leave the EU on 29 March, but the exit deal that Mrs May negotiated with the EU was rejected by 432 votes to 202 on Tuesday.
That vote saw more more than 100 Conservative MPs - including three Scottish Tories - joining the opposition parties in voting against the government.
Ms Sturgeon wants the UK's departure from the EU to be delayed to allow a second EU referendum to be held which could allow the country to remain.
She also said it was "increasingly clear" that "Scotland's interests will only be protected with independence", and that she would give more details on the timing of a second independence referendum in the "next matter of weeks".
Scottish Conservative MP Ross Thomson - who opposed the Brexit deal on Tuesday but backed the government in Wednesday's vote - claimed that the SNP only want to "disrupt Brexit as much as possible and use it as a tool to enhance their chances of holding and winning a second independence referendum".
'Cleared the air'
His party's interim leader in Scotland, Jackson Carlaw, said the result of the confidence vote had shown that Mrs May is the "right woman to take us forward, and means she can secure an orderly departure from the EU."
He added: "This vote has cleared the air, and now we can focus on what really matters - making Brexit work for Scotland and the rest of the UK."
Meanwhile, Scottish Liberal Democrat leader Willie Rennie repeated his calls for Labour to join his party and the SNP in backing another EU referendum.
Mr Rennie said: "There is now nowhere left for the Labour leadership to hide. They must listen to the overwhelming majority of Labour supporters and back a People's Vote."