Trump also reiterated his belief that new regulations would open the door for China to outpace the United States in AI advancement.
Although he acknowledged Amodei's concern that going too fast on AI could expand risks, Trump said it's more important for the United States to maintain a technological edge over China.
"We're about maybe a year and a half up on China," Trump told Fox News while attending the Presidents Cup golf tournament in Illinois on Sunday.
"We're leading, and we're building tremendous, trillions of dollars' worth of places. And why should we give that up?"
Trump, confirming earlier reporting by Axios and Reuters, told Fox News that he would have dinner with Amodei on Sunday night.
The meeting comes as the CEOs of Anthropic rivals have called for slowing development of increasingly capable AI systems. These include OpenAI, Google's DeepMind, Microsoft and xAI.
A groundswell has risen in favour of federal intervention after OpenAI said in July that an autonomous AI agent went rogue during a security test and hacked into another company.
Incidents of rogue AI agents are not a cause for alarm, Trump told Fox News.
"I don't worry about it," he said, adding that he remains confident in the technology and its potential.
Amodei is not the only major tech figure trying to bend Trump's ear on AI regulation.
In an interview that aired earlier on Sunday on NBC's Meet the Press, Microsoft co-founder Bill Gates said he would like to meet with Trump to discuss AI.
"I hope that, given my life's work in the field, my saying how unique and different this is and how concerned I am will add to what he's hearing from other people," Gates said, echoing calls by Amodei and others for new AI regulations.
"You need law enforcement and the politicians to get into the discussion about what safeguards and monitoring look like," Gates said in a taped interview.
"And that has to be a required thing."
Trump has previously described the chorus of AI concerns as a "hoax".
Gates argued that safeguards would not dramatically hinder the industry, and that the risks of not implementing them are real.
"It's not a hoax at all," Gates told NBC.
In a rare show of unity, the CEOs of rivals Anthropic, OpenAI, Google's DeepMind, Microsoft and xAI have called for slowing the development of increasingly capable AI systems.
Former Anthropic researcher Jacob Coxon warned that AI could kill us all by the end of the decade, prompting US lawmakers to call for new rules to govern the technology.
