Fifa has said there remains "significant work to be done" to ready Russia for hosting the World Cup now just over seven months away.
The world football governing body believes Russia's preparations are on track to be completed in time for the tournament, but that risks remain.
Fifa's diagnosis echoed comments by Russia president Vladimir Putin who warned his countrymen earlier this week that "if we relax, we will not fully accomplish the work".
Seven World Cup stadiums are yet to be completed in Russia and many have been beset by spiralling costs.
"Obviously we are looking at the readiness not only of the stadiums but of all the host cities," said Smith.
"We look at training sites, hotels, airports, general road infrastructure. In general, the state of readiness is good, planning is good and on track. But as we have said at numerous stops there are risks still.
"There is a significant amount of work to be done, especially in the next two or three months, to have all the contruction and some of the commissioning works completed by the end of the year."
With some yet-to-be-finished having well extended their expected completion dates, Russian president Vladimir Putin moved to play down concerns that Russia will not be ready for the tournament.
"These delays are not critical, there is nothing terrible there," said Putin.
"It is the most difficult thing to resolve tasks at a final stage. If we relax, we will not fully accomplish the work."
The Russia World Cup, over which their are also fears over hooliganism and racism, begins next June and has designated 12 stadiums across 11 cities to host games.
England have booked a base camp at a four-star hotel near St. Petersburg.