My mom said she was there on a field trip between June and August of 1968 and said there were protesters between the washington monument and the lincoln memorial. She's always been curious about what was happening that summer.
So earlier in April Dr. King had been killed in Memphis and many American cities experienced protests that had turned violent at times, including DC. So it is entirely possible it was residual to that.
But the fact is that lots of events happen all the time on the Mall, almost every day there is someone out there protesting something. Just as it is true in our politically charged current time, so was it in the late 60's.
TO give you an idea of just how many different groups or causes it might have been, here is just a partial list of the various marches and rallies scheduled in 2017 for the Mall or surrounding streets. https://www.eventbrite.com/d/dc--washington/rallies/?crt=regular&sort=date
Today the 18th: Syrian Revolution Anniversary Rally
March 28th: 1st Annual March to End Child Abuse
April 22: The whole March for Science thing, and counter protests.
April 29th; People's Climate March
May 14th; March for Moms
And that is just in the next 3 months. So without being able to narrow down the dates more it is likely going to be very difficult to find out the precise group or event it was.
Were the protesters black (or mostly black)? The timeframe suggests it could have been the poor people's campaign, which was a major civil rights demonstration where some protesters camped on the mall for an extended period.