Led by Youth Congress Deputy President Prakash Gujjar, they took out a procession in Khanpur area, burnt Modi's effigy in front of BJP office, and locked the gates.
Police had to intervene to open the gates.
"Today we have locked BJP office, tomorrow people of the state will throw out BJP government," NSUI member Indravijaysinh Gohil said.
"Despite 16,000 children being kidnapped and going missing (in the last few years), the BJP government has remained insensitive to the issue and has done nothing to get them back," Gujjar said.
Instead of giving sympathy to the parents, Modi had them arrested when they tried to meet him, he said.
Youth Congress had given a bandh call for schools and colleges today in rest of Gujarat (barring Ahmedabad) on the issue.
Schools and colleges in Rajkot district remained closed, but in other regions the response was mixed, sources said.