Fifa said on Sunday Russia could continue to play matches in neutral venues and only under the name Football Union of Russia (RFU), but warned the country could be excluded from competitions if the situation in Ukraine does not improve.
The announcements, which Fifa called "immediate first measures" were, however, swiftly criticised as insufficient by the head of the Polish Football Association.
Poland has said it will not play against Russia in their scheduled World Cup qualifying playoff on March 24 in protest about the invasion of neighbouring Ukraine.
Fifa, who condemned the "use of force by Russia in its invasion of Ukraine", said no international soccer matches will be played in Russia and the country's flag and anthem will be banned from their matches abroad. The global governing body said the national team would not compete as Russia but as the RFU and "home" games would be held without fans on "neutral territory".
Polish Football Association chief Cezary Kulesza criticised Fifa's stance and called for Russia to be expelled from the World Cup.
"Today’s Fifa decision is totally unacceptable. We are not interested in participating in this game of appearances. Our stance remains intact: Polish national team will not play with Russia, no matter what the name of the team is," he wrote on Twitter.
"If Fifa's human rights policy is more than just words on paper, now is the time to put it into effect, excluding the RFU from qualifying for the Qatar World Cup in 2022," he said.
The Czech Republic and Sweden, who are in the same play-off path as Russia and Poland, have also said they would not play against the Russians. Fifa said it would try to find a solution with the three countries involved in the World Cup qualifiers.
"Fifa has already engaged in dialogue with all these football associations. Fifa will remain in close contact to seek to find appropriate and acceptable solutions together."
England's Football Association also said its national team would not play any matches against Russia "for the foreseeable future".
"Out of solidarity with the Ukraine and to wholeheartedly condemn the atrocities being committed by the Russian leadership, the FA can confirm we won’t play against Russia in any international fixtures for the foreseeable future. This includes any potential match at any level of senior, age group or para football," a spokesperson said.
Fifa's statement did offer the prospect of further sanctions.
"Fifa will continue its ongoing dialogue with the International Olympic Committee (IOC), Uefa and other sport organisations to determine any additional measures or sanctions, including a potential exclusion from competitions, that shall be applied in the near future should the situation not improve rapidly."
On Friday the IOC urged international sports federations to either move or cancel events planned in Russia and Belarus.
Russian troops entered Ukraine through Belarus when the invasion started on Thursday. Ukrainian forces were holding off Russian troops advancing on the capital Kyiv, Ukrainian President Volodymyr Zelenskiy said as the biggest assault on a European state since World War 2 entered a fourth day.
