The Catalan politicians face an array of charges ranging from misuse of public funds to rebellion, the most serious crime, which carries a maximum prison sentence of 30 years upon conviction.
Riot police used batons to keep the demonstrators away from the federal government offices in Barcelona.
Tensions in Catalonia are very high and its separatist leaders have abandoned plans to name a new president following the arrest of the latest candidate.
Other separatist figures were already in custody or had gone into exile overseas.
He and other secessionist leaders are due to appear before the Supreme Court on Friday morning for the opening of a new phase in the investigation which precedes a trial.
Thousands of protesters have filled the streets of Barcelona carrying the single-star flag of the presumptive Catalan Republic with signs and slogans such as "Freedom for Political Prisoners".
In a statement, the court said the indictment concerns activities going back six years created to "execute a predetermined plan with the aim of declaring Catalonia's independence, outside of the law".
Protestors tried to break through police lines.
But one of them, Marta Rovira, ignored the summons and instead announced she was taking "the road to exile".Rovira is deputy leader of the leftwing separatist ERC party, whose chief is now in jail.
As well as the 13 people facing rebellion and sedition charges, another 12 will be tried for alleged embezzlement or for disobeying the state, for their role in holding the independence referendum. They deny the allegations.
All five spent some time in detention following the banned referendum but were released on bail late previous year pending investigations into their individual roles in the banned referendum.
A Supreme Court judge held former Catalan parliament president Carme Forcadell and three former regional ministers alongside Turull. He did not set a date for their trial.
Four other separatists had already been detained by the Spanish authorities.
The Spanish government refused to comment on the decision.Reports of the Spanish media said Turull has asked the Catalan regional assembly not to suspend Saturday's investiture debate.
However, on Friday, Llarena issued fresh orders for European and worldwide arrest warrants for Catalan politicians overseas, including Puigdemont and Rovira.
"Exile will be a hard road, but it is the only way I have to recover my political voice". She issued a letter explaining why she had chosen "the path of exile", but Judge Llarena later added her name to his list of worldwide arrest warrants.
Most prominent among them is Carles Puigdemont, Catalonia's ex-president, who has been living in Belgium since October.
Later on Friday, Catalan parliament speaker Roger Torrent said he would read a statement in support of those in prison in the parliamentary session.