The spokesman added that the two leaders discussed the international response to the virus, including "UK-US cooperation in the fight against the pandemic" and also "committed to continue working together to strengthen our bilateral relationship, including by signing a free trade agreement as soon as possible".
Raab will deputise for Johnson at tomorrow's Prime Minister's Questions and will also chair a Cabinet meeting in his absence, but there is an increasing expectation that Johnson will return to Number 10 next week.
The Prime Minister's spokesman said he was continuing his recovery at Chequers, but was now "receiving updates and making calls" in a clear sign he is increasing his workload every day.
Johnson will speak to the Queen by phone later this week, resuming his weekly audiences for the first time since he fell ill. Raab has not been in contact with the Queen in Johnson's absence.
Johnson has also been holding meetings with aides at Chequers and held a two-hour meeting with Raab last week.
Sources have said he has asked for policy papers on domestic and international issues, as he gets himself up to speed on developments across Government in the time he has been on sick leave.