I was going to cut and paste some of a previous answer I wrote on 1990s Russia, but it's actually probably worth just writing up something new.

The thing to keep in mind is that with the dissolution of the Soviet Union and the folding of the remaining Soviet governmental institutions into Russian ones with Gorbachev's resignation, a federal level of the Soviet system was abolished, but technically just this one level. The Russian Soviet Federative Socialist Republic had been renamed the Russian Federation - but it was still operating under its Soviet-era 1978 constitution, which was in turn modeled after the Soviet constitution. The RSFSR constitution had itself been heavily amended to reflect Gorbachev-era changes - a directly-elected office of President had been added, for example - but fundamentally it was the same Soviet system with new parts tacked on. The legislature of the new Russian Federation was a Congress of Peoples Deputies that had been elected in 1990 in free-ish multicandidate (but not multiparty) elections. This Congress (CPD) consisted of 1,068 deputies who were supposed to meet twice a year to discuss major constitutional issues (a 2/3 vote could change the constitution), and who in turn elected a more permanent Supreme Soviet of 248 voting and 138 non-voting members (although by September 1993 a quarter of the total members were inactive): this Supreme Soviet in turn was divided into a Soviet of the Republic and a Soviet of Nationalities, which functioned like a lower and upper house. A Chairman of the Presidium was also elected, and this person until 1991 was effectively the Head of State of the RSFSR: Boris Yeltsin held this position from 1990 to July 1991, when he was elected to the new position of Russian President, and the Chairman position was supposed to become something more like a Parliamentary speaker. The Speaker was the fourth most powerful figure after the President (Yeltsin), the Vice President (Alexander Rutskoi), and the Prime Minister (Yeltsin himself initially held this job before Yegor Gaidar became Acting Prime Minister - the President nominated the PM but the Supreme Soviet was supposed to vote to confirm). Yeltsin ally Ruslan Khasbulatov took the job - we'll hear more about him later. In any case, this Soviet-era legislature was the sitting legislature of the new Russian Federation, and had a mandate through 1995.

The Supreme Soviet had effectively self-marginalized itself by creating and giving powers to the Presidency in 1991, and in November by effectively giving the Presidency temporary emergency powers to form a government under Gaidar to push through "Shock Therapy" economic reforms (such as the liberalization of all prices on January 2, 1992). This was in theory couched by legislation that the President did not have the right to dissolve or suspend the Supreme Soviet, that the President should report at least once a year to the CPD, and that no governmental acts should infringe existing legislation. Ultimately the amended constitution gave both the legislature and executive claims to supreme state power, and the issue turned into a political contest as much as a legal/constitutional one.