Said had also been investigated by US authorities over fundraising for Hamas, a Palestinian political faction, the newspaper reported.
US Muslim groups said the resignation was the result of a campaign to discredit Muslims' involvement in politics.
Ibrahim Hooper, a spokesman for the Council on American-Islamic Relations, told Al Jazeera the resignation was "symptomatic of the efforts of a vocal minority to exclude Muslims from the political process".
"They use smear tactics to attack Muslims who want to take part in the political process," he said.
Hooper said that Muslims were becoming better organised politically and that that may be the reason for the increase in attacks on them.
Obama had apologised to two Muslim women wearing headscarves who were prevented from sitting behind his podium by campaign volunteers during a speech in Detroit in June to stop them appearing in photographs of the event.
Salam Al-Marayati, the executive director of the Muslim Public Affairs Council, where Asbahi had previously worked, told Al Jazeera that the resignation was symptomatic of a deeper problem in US political culture.
"People have to be exposed to the truth. They don't believe us when we talk about Islamophobia. They say we're whining or into self-victimisation. Things like this prove that's not true."