Nicola Sturgeon is travelling to California, as part of a five-day visit to the United States.
She has been invited to give a speech at Stanford University on Scotland’s place in the world.
The Scottish Conservatives have questioned Ms Sturgeon’s priorities, saying she should “get back to the day job”.
The first minister will also meet Governor of California Jerry Brown to discuss climate change.
Mr Brown has criticised President Trump for his executive order overturning many climate change policies introduced by President Obama.
The Scottish parliament has started its Easter recess.
A Scottish government spokeswoman said: “The First Minister’s visit will focus on promoting trade and investment, boosting tourism, sharing best practice across the public and private sector and promoting Scottish innovation and entrepreneurship.
“The relationship between Scotland and America is an important one with deep and long-standing ties reflected by the strong economic, cultural and personal links of our citizens.”
Conservative MSP Annie Wells said she fears the first minister will use the trip to promote Scottish independence.
She said: “The First Minister seems determined to talk about independence at every opportunity she gets.
“Rather than going abroad to try and sell her plans for separation, she should accept that Scots don’t want a second independence referendum and get back to the day job of improving our health service and schools.”
The start of the first minister’s trip has coincided with further comments from the Spanish government about its attitude to Scotland joining the EU.
Spain has confirmed that it would not initially block any attempt from Scotland to join the EU after Brexit.
Foreign Minister Alfonso Dastis, however, said he remains opposed to independence.
Mr Dastis added: “Having said that, if, in application of its laws, the outcome of that process is a division of the United Kingdom, any part of the United Kingdom that becomes a state and wants to join the EU will have to apply. And follow the steps that are stipulated.”
He warned an application for membership could take several years to be processed.
SNP MP Stephen Gethins said: “This is a significant intervention by Spain’s foreign minister which confirms what other Spanish politicians have said previously.
“We can be now absolutely clear – there is no intention of a ‘Spanish veto’ over Scotland’s EU membership.
“This is just the latest indication from a senior European diplomat that an independent Scotland would be welcomed into the EU, after Lord Kerr this week said that we’d be in ‘very fast’.
“EU countries want to be constructive with Scotland and will respect the democratic will of the Scottish people if we choose to be independent.”
The Conservatives have said the issue was not just about the exercise of a veto.
MEP Ian Duncan said: “The issue about an independent Scotland’s EU membership has never been about an individual country’s veto.
“The truth is the decision would rest in the hands of all 27 member states, each of which would undoubtedly ask for something from Scotland in return.
“This is likely to lead to sweeping concessions, especially for our fishermen. This would result in a hugely unfavourable deal, something considerably worse than the UK’s membership of the EU prior to Brexit.”