Russia, which hosts the world's most-watched sporting event for the first time this year, is a key backer of Syrian President Bashar al-Assad's regime and arguably the most powerful broker in the seven-year-old war.
"In hosting one of the most televised events in the world, Russia is courting world public opinion and looking for respect," HRW's executive director, Kenneth Roth, said in a statement.
"World leaders should signal to President Putin that unless he changes track and acts to end atrocities by Russian and Syrian forces in Syria, they won't be in their seats in the VIP box with him on opening night."
Billions of people worldwide are expected to watch the World Cup on television and HRW argued that Moscow's responsibility in the suffering of Syrian civilians should not be forgotten.
Russia is the main exporter of weaponry to the Syrian regime and its forces provide on-the-ground support to government forces and allied militia.
The New York-based watchdog has documented Russian-Syrian joint military operations that "have caused thousands of civilian casualties", including recently in Eastern Ghouta near Damascus.
Roth warned that millions of other civilians faced the same fate in upcoming operations, especially in the northwestern province of Idlib that still largely escapes government control.
"World leaders should not allow a sporting event to gloss over a pattern of atrocities in Syria that now looms over two million civilians," he said.
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