Nicola Sturgeon is due to meet Theresa May and Westminster opposition leaders later to discuss Brexit.
Speaking ahead of the London visit, the first minister said her aim was to discuss a “workable alternative” to Mrs May’s proposed agreement.
The prime minister has insisted the draft agreement is the only realistic chance of avoiding a no-deal Brexit.
Ms Sturgeon has already said SNP MPs will vote against the deal in the House of Commons.
There has been widespread criticism of the draft 585-page withdrawal agreement and the short paper setting out what the UK and EU’s future relationship could look like.
Two of the prime minister’s cabinet ministers have resigned, while others are believed to be trying to change its wording, and there is talk of a Tory leadership challenge.
Scottish Secretary David Mundell has said he is backing the plan, even though it was “not a perfect deal”, because the alternative of leaving the EU without an agreement would be “catastrophic” for Scotland.
Ms Sturgeon, however, said the prime minister and her allies were presenting a “false choice” between the agreement and a no-deal Brexit.
She said: “This is a time for grown-up, responsible governance in the public interest – something which has been sadly lacking to date as the Tory party has continued to put its own interests ahead of the interests of jobs, communities and businesses.
“It mustn’t be an option between frying pan or fire – but it is now incumbent on all of us who oppose that false choice to propose a workable alternative.”
In interviews at the weekend, Ms Sturgeon suggested two ways forward – for the House of Commons to coalesce behind a plan to keep the UK within the single market and the customs union, and the option of a second vote.
She also said she was willing to engage with opposition leaders, including Jeremy Corbyn, to offer a “clear alternative”.
On Monday, Theresa May tried to persuade business leaders that the deal offered the best way forward, saying it would stop EU migrants from being able to “jump the queue”.
She told the CBI conference in London that migration would become skills-based, with Europeans no longer prioritised over “engineers from Sydney or software developers from Delhi”.
Ms Sturgeon later tweeted that she believed the prime minister’s choice of words was “offensive” and “disgraceful”.
Jeremy Corbyn told the same conference that Brexit could be a “catalyst for economic transformation” in the UK.
Labour has said its priority is to secure a general election, and argued that there was still time to secure a better Brexit deal.