"The opportunity for that call is not yet. But we'll be patient," the prime minister told reporters in Washington DC on Thursday morning.
"We understand their disappointment and that is the way that you manage difficult issues. It's a difficult decision."
Australia was accused of blindsiding France over the decision to ditch a deal to acquire conventional submarines from French company Naval Group.
France recalled its ambassadors from Australia and the US in retaliation to the announcement.
In a subsequent call with France, Mr Biden agreed consulting that country ahead of the announcement could have prevented the diplomatic row.
Mr Morrison welcomed the US call, which he said helped reinforce the important role France and Europe played in the Indo-Pacific.
"Our door is wide open. Our invitation is there. We understand the hurt and the disappointment," he said.
But the prime minister expected to wait a while for his own chat with Mr Macron.
"I know that will be some time before that occurs, but we will patiently pursue those opportunities because we want to work together," he said. "I look forward when the time is right and when the opportunity presents that we will have a similar discussion."
Mr Morrison was also confident of securing the necessary political backing from US politicians for the sharing of nuclear technology after meeting with House Speaker Nancy Pelosi.
"The support on the Hill, of course, in the US system of government, will be absolutely necessary as we progress this important partnership," Mr Morrison said.
He will meet world leaders including Japanese Prime Minister Yoshihide Suga and Indian Prime Minister Narendra Modi in Washington.
Mr Morrison will also take part in a virtual meeting with Pacific Islands Forum leaders and United Nations Secretary-General Antonio Guterres.