A statement made on Saturday by OpenAI claimed, external its agreement with the Pentagon had "more guardrails than any previous agreement for classified AI deployments, including Anthropic's".
But on Monday, Altman posted on X to say further changes were being made, including making sure its system would not be "intentionally used for domestic surveillance of U.S. persons and nationals".
As part of the new amendments, intelligence agencies such as the National Security Agency would also not be able to use OpenAI's system without a "follow-on modification" to the contract.
Altman added the company had made a mistake by rushing "to get this out on Friday".
"The issues are super complex, and demand clear communication," he said.
"We were genuinely trying to de-escalate things and avoid a much worse outcome, but I think it just looked opportunistic and sloppy."
OpenAI has faced backlash from users following its announcement it was working with the Pentagon.
According to data from Sensor Tower, the number of people uninstalling ChatGPT has surged since the news of OpenAI's partnership with the Department of Defense was announced on Friday.
The market intelligence firm said the daily average uninstall rate was up by 200% compared to normal rates.
Meanwhile, Anthropic's Claude rose to the top of Apple's App Store ranking, where it still remains on Tuesday, external.
The AI model was blacklisted by the Trump adminstration following Anthropic's refusal to drop a corporate "red-line" principle that its technology should not be used to create fully autonomous weapons.
Despite this, the use of Claude in the US-Israel war with Iran has since emerged, external, with BBC News' US partner CBS News reporting it was still in use on Tuesday.
The Pentagon has declined to comment on its dealings with Anthropic.
AI is used in a number of ways in the military, for example streamlining logistics or quickly processing large amounts of information.
The US, Ukraine, and Nato all use tech from Palantir, an American company which provides data analytics tools to government customers for intelligence gathering, surveillance, counterterrorism and military purposes.
The UK Ministry of Defence recently signed a £240m contract with the firm.
At the end of last year, the BBC spoke to some of those involved in integrating Palantir's AI-powered defence platform Maven into Nato.
The software brings together a huge range of military information, from satellite data to intelligence reports, which can then be analysed by commercial AI systems such as Claude to help make "faster, more efficient, and ultimately more lethal decisions where that's appropriate"said Louis Mosley, head of Palantir's UK operations.