* Students block traffic on Danube bridge, roads
* Second student protest within a week against tuition
* Gov't wants to cut state-financed places in higher education (Adds detail, comments)
By Krisztina Than and Marton Dunai
BUDAPEST, Dec 12 (Reuters) - Thousands of students rallied on Wednesday against the Hungarian government's planned sharp cuts in state-financed places at universities, blocking peak traffic on one of the main bridges in Budapest and several roads in freezing weather.
The students, staging the second spontaneous protest march through the Hungarian capital this week, are demanding that the government give up its plans to cut funding to higher education and start a public dialogue about the reforms.
Hungary's centre-right government is trying to keep the budget deficit below the European Union's 3 percent ceiling amid a recession in central Europe's most indebted economy.
The protest march, which started with a meeting at Budapest's University of Technology and Economics, rapidly grew and headed to the Economy Ministry in sub-zero temperatures.
The students, shouting "Down with the tuition" and "Honk if you are with us", demanded that officials come out to meet them. They also demanded the resignation of education secretary Rozsa Hoffmann. Then they headed onto Parliament.
Police did not interfere.
"The biggest problem is the dictatorial system which is disguised as democracy, that people do not have a say in their own country's legislation," Balazs Tahi-Toth, 22, who is studying to be an engineer, told Reuters. "This was just the last drop."
Prime Minister Viktor Orban's government announced the planned cuts in higher education last week. From next year it plans to fully finance only 10,480 students, two-thirds fewer than this year. It will partly finance the tuition of 46,000 more and offer subsidised preferential-rate student loans.
Students fear this will shut out many from higher education and force many more students to seek a place at a university in those European Union states where education is free, such as in neighbouring Austria. They pledge further protests next week.
"I have three younger sisters who want to go to higher education and it does not seem that we will be able to pay the tuition or take out a student loan... I don't think it would be a responsible idea to become indebted in this debt crisis," said Zsombor Cseh, 22, a student at Budapest's Corvinus University.
"This loan would solve the problem only if we could be sure that we will find a decent job with a decent pay."
The government, which has used a two-thirds majority in parliament to rewrite large swathes of laws including the constitution in ways that critics say cement the ruling party's powers, is denying it is introducing tuition.
"The new higher education concept is based on a system in which the state will finance everyone's studies, either by granting them scholarships or a new type of student loan," the Prime Minister's Office said in a statement on Tuesday.
The students invited Orban for a discussion on Wednesday but he only replied in a brief letter.
At the meeting earlier on Wednesday, students screened videos of Orban from 2007 and 2008 when his Fidesz party was still in opposition and spoke out against tuition - which the then ruling Socialists wanted to introduce. Fidesz initiated a referendum against the tuition and successfully blocked it. (Reporting by Krisztina Than; Editing by Michael Roddy)