BRUSSELS—Former British Prime Minister Tony Blair said the West must work with Russian President Vladimir Putin on Islamist extremism and other sources of conflict in the Middle East—even as it takes a strong line with Moscow over its actions in Ukraine.

In an interview in Brussels on Tuesday, Mr. Blair described Islamist extremism as “the largest long-term security threat we face” and said the West had to be ready to cooperate with Moscow and other countries such as China and India to confront it.

Europe couldn’t be indifferent to the annexation of the territory of a country on its doorstep, he said, but “Russia remains a powerful player, and in certain areas including the Middle East at the present time they are an important component of how we deal with these challenges.” Russia would likely have to be involved in finding a solution in Syria, he said.

In the interview, he declared himself more worried about the Israel-Palestinian situation than at any time since he took over his role as special Middle East envoy in 2007.

He said moves in Europe to recognize a Palestinian state was “an expression of the frustration people feel at the absence of progress and also the anxiety people feel about the treatment of Palestinians.” Sweden, for instance, recognized Palestinian statehood last month, and such a measure is under debate in other countries. “The government of Israel would be sensible to take account of the strength of that opinion,” he said.