One piece of legislation bars the so-called 'against-all' option on ballots - a staple in elections since the early 1990s that has allowed Russian voters to express their dissatisfaction with the political process.
The second bill would strip legislators of their seat if they switch parties and prohibit parties from supporting candidates from other parties at elections - seen by critics as a Kremlin attempt to weaken an already disorganized and embattled opposition.
The legislation barring against-all votes passed 347-87, while the second bill passed 378-57. To become law, the bills must be approved parliament's upper house and be signed by the president, the AP reports.
There are several versions of the recent assassination of the most prominent Iranian nuclear scientist and high-ranking officer of the Islamic Revolutionary Guard Corps, Mohsen Fakhrizadeh