"We decided to stop all kinetic activity," the source told Axios, using a military term for airstrikes, for example.
Another American source told the site that both sides agree to return to the ceasefire, "for now."
According to the sources, representatives of the United States and Iran will resume so-called technical talks in the Qatari capital, Doha, on Tuesday. The situation around the Strait of Hormuz will be discussed.
Tuesday's talks were originally scheduled to take place in Switzerland and focus on Iran's nuclear program, but the escalation in recent days has refocused the talks on the crucial strait, according to Axios' sources.
The White House has not commented on the information.
The United States has launched new attacks on Iran this weekend, while Iran has responded by attacking American bases in countries such as Bahrain and Kuwait.
The latest escalation came on Thursday, when a ship sailing through the Strait of Hormuz was reportedly attacked by an Iranian drone. Iran and the Revolutionary Guard have described the ship as violating the rules set by the Iranians.
The countries have accused each other of violating the ceasefire and the terms of the declaration of intent they signed on June 15. That agreement is intended to be a first step in the process towards a lasting peace.
