The group were intercepted by police and forcibly removed.
The incident occurred after a day-long demonstration on Saturday, attended by tens of thousands of people opposed to the wearing of masks and other government measures to try and limit the spread of coronavirus.
Police ordered the protesters to disband halfway through their march around Berlin after participants refused to observe social-distancing rules - but a rally near the capital’s Brandenburg Gate took place as planned.
Footage of the incident showed hundreds of people, some waving the flag of the German Reich of 1871-1918 and other far-right banners, running towards the Reichstag building and up the stairs.
Police confirmed that several people had broken through a cordon in front of Parliament and “entered the staircase of the Reichstag building, but not the building itself”.
Police had "stones and bottles" thrown at them according to the force, with officers having to use "force [...] to push them back."
Earlier in the day, thousands of far-right extremists had thrown bottles and stones at police outside the Russian Embassy. Police detained about 300 people throughout the day.
Berlin's regional government had tried to ban the protests, warning that extremists could use them as a platform and citing anti-mask rallies earlier this month where rules intended to stop the virus from being spread further were not respected.
Protest organisers successfully appealed against the decision on Friday, though a court ordered them to ensure social distancing.
During the march, which authorities said drew about 38,000 people, participants expressed their opposition to a wide range of issues, including vaccinations, face masks and the German government in general.
Some wore T-shirts promoting the “QAnon” conspiracy theory, others displayed white nationalist slogans and neo-Nazi insignia.
Most participants, however, denied having far-right views.
Germany has seen an upswing in new Covid-19 cases in recent weeks.
The country’s disease control agency reported on Saturday that Germany had almost 1,500 new infections over the past day.
Germany has been praised for the way it has handled the pandemic, and the country’s death toll of some 9,300 people is less than one-fourth the amount of people who have died of Covid-19 in the UK.
Opinion polls show overwhelming support for the prevention measures imposed by authorities.