Abbas Alawieh, an uncommitted delegate from Michigan, was emotional as he relayed the news outside the United Center, where the convention concludes on Thursday.
“We were hopeful because Vice-President Harris’s team was engaging with us,” Mr Alawieh told reporters. “We just want to be heard.”
The uncommitted delegates were selected in state Democratic primaries earlier this year – part of an internal party protest against US support for Israel.
President Joe Biden won an overwhelming share of primary voters, but pro-Palestinian activists urged people to vote “uncommitted” and similar options in a number of states.
Enough Democratic voters did so to send 30 delegates to the convention in Chicago, out of a total of more than 2,400 delegates.
Mr Alawieh said it was “unacceptable” that their request for a speaking slot was turned down.
“We’re not going anywhere before November,” he said. “You’re not going to get rid of us. We’re going to engage the system.”
After they announced that their request had been rejected, Mr Alawieh and three other uncommitted delegates began a sit-in outside the arena.
The delegates also said that they had collected signatures from nearly 250 Harris delegates supporting a ceasefire in Gaza.
The war in the Middle East has been the main focus of a series of protests outside the Democratic convention this week.
On Monday several thousand protesters marched by the United Center, although the turnout was less than organisers had expected.
A smaller protest held outside the Israeli consulate in Chicago on Tuesday led to clashes between protesters and police, resulting in 56 arrests.
Another march outside the convention site is planned for Thursday evening.
Cook County, where Chicago is located, is home to the country’s largest Palestinian community.
A group of pro-Palestinian Democrats said their request for a speaking slot at this week’s Democratic National Convention has been denied by party leaders.
The “uncommitted” delegates were hoping as late as Wednesday evening that a Palestinian-American politician would be allowed to speak critically about Israel’s war in Gaza.
But a spokesman for the Uncommitted National Movement said their request was turned down.
The BBC contacted Kamala Harris’s campaign for comment.