Musk tweeted his support earlier this week for Tillerson in the role of secretary of State, a Trump administration choice that has raised hackles among environmentalists as well as skeptics who point to Tillerson's business ties to Russia.
Here is a bit of what he said:
"Tillerson obviously did a competent job running Exxon, one of the largest companies in the world. In that role, he was obligated to advance the cause of Exxon and did. In the Sec of State role, he is obligated to advance the cause of the US and I suspect he probably will. Also, he has publicly acknowledged for years that a carbon tax could make sense. There is no better person to push for that to become a reality than Tillerson. This is what matters far more than pipelines or opening oil reserves. The unpriced externality must be priced."
The comments mostly echo or repeat things Musk said on Twitter earlier this week, when his initial support of Tillerson led to some to criticize Musk.
It is true that Tillerson has publicly acknowledged that the climate is changing and that emissions are a factor. During a speech in 2009, he said that a carbon tax is "the most efficient means of reflecting the cost of carbon in all economic decisions — from investments made by companies to fuel their requirements to the product choices made by consumers."
However, Tillerson also stressed the need for "a uniform standard to hold all nations accountable," saying that the challenge of climate change is global, and that nations developing now are likely to generate a considerable amount of carbon emissions in the future.
As secretary of State, Tillerson would have a key role in negotiating international climate treaties such as the Paris Agreement. However, President Donald Trump had promised to "cancel" the agreement while a candidate, though he later said he had an "open mind" on the issue.
Musk has been a vocal supporter of a carbon tax, and has repeatedly referred to carbon emissions as an "unpriced externality." By this he means that the effects carbon pollution have on the environment (such as climate change/global warming) constitute a cost someone is going to end up paying for.
Taxing carbon emissions, therefore, pays for or at least offsets the larger environmental costs of a changing climate.
Of course, many are doubtful that the former ExxonMobil chairman and CEO will actually deliver a carbon tax, domestically or otherwise.
Climate scientist and Pennsylvania State University professor Michael Mann responded to Musk's tweets with skepticism:
A Tesla spokesperson said the company had no further comment beyond Musk's remarks.
More From CNBC