Qatar is under strict sanctions from Saudi Arabia and its allies, who have sent it a list of 13 demands it must meet before sanctions are lifted.
Among the demands are that Qatar shutter its Al Jazeera news network and cut back ties to Iran.
The Arab states involved all have close ties with the US, but the US State Department and Secretary of State Rex Tillerson have yet to make a formal statement on the demands that were made public on Friday.
"The four countries that are part of that - we believe it's a family issue and that they should work [it] out," said Mr Spicer.
"If we can help facilitate those discussions then so be it. They want to, and should work out for themselves."
Mr Tillerson had been expected to address the issue on Friday.
He had previously anticipated the release of a list of demands from the Saudis and their allies: Bahrain, Egypt and the United Arab Emirates.
The countries want Qatar to comply to the 13 orders before they will lift severe sanctions, which were first imposed on it earlier this month.
They say Qatar is funding terrorism and fostering regional instability, accusations it denies.
The Qatari foreign ministry confirmed early on Saturday that it had received the list of demands, and would now "prepare an appropriate response."
US President Donald Trump has taken a hard line towards Qatar, accusing it of being a "high level" sponsor of terrorism.
However, the largest US base in the Middle East is in Qatar, meaning it is caught in the middle.
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