Martinez, who has been openly critical of some of Trump's policies and remarks on immigration, told local reporters Monday that she is "really busy" and will skip Trump's rally in Albuquerque.
"I'm the governor of New Mexico and I'm really focused on what's going on here in New Mexico -- just like the announcement we just did with 100 new high-tech and research jobs, improving the education for our kids, another job announcement tomorrow. Those are the things that I'm concentrating on and I'm going to keep concentrating on," Martinez told reporters, according to the Albuquerque Journal.
Trump seemed to take aim at Martinez during his rally Tuesday night, joking that maybe he would run for governor of New Mexico.
"We gotta get her moving," he said, adding later that Syrian refugees are being brought to New Mexico and if he was governor, such a thing wouldn't happen.
Martinez, who chairs the Republican Governors Association, has yet to endorse Trump. She previously supported Florida Sen. Marco Rubio's presidential bid.
Martinez is not the only prominent Republican holding out support for Trump.
Most notably, House Speaker Paul Ryan has also yet to endorse the de facto Republican nominee. Ryan has met with Trump since announcing he was not yet prepared to back the New York billionaire's candidacy, but has said work still remains to unite the party.
Other Republicans in New Mexico are beginning to rally around Trump's candidacy, though.
Trump is holding his first official fundraiser for his presidential bid -- as part of his joint fundraising agreement with the RNC -- in the state Tuesday before his rally.
GOP donors will need to contribute $10,000 to attend the reception, which also earns them a photo with the candidate, according to a copy of the invitation obtained by CNN.